Though your request is scant on actual examples of this mom's problems, a couple of things jump out at me from your description. First, this sounds like a very spirited and active child, and a mother who sounds pretty discouraged and is probably sampling any form of discipline she can think of.
If the mom herself is labeling her child as "not very nice" or even harsher labels, she's setting herself and her child up for failure. A child will live down (or up) to a parent's expectations, and if she hears a poor assessment of herself, then that's what she's likely to aim for. If you're bad, why try?
The child may also be over-scheduled, or inappropriately scheduled, for her age and personality. Some 3-4 year-olds are not yet capable of staying focused through an hour-long class of any sort, and it's a waste of time and money to enroll them until they can. Toddlers and young children learn primarily through free play, and can hardly get enough of it. It's what they are programmed to do. Classes, especially if the child hasn't had enough physical exercise and imaginative play, could just be asking too much.
I'm also guessing this little girl is not feeling especially valued in her family, and is acting out to get the attention she craves. She may feel displaced by the baby brother, and unfairly punished for seeking attention – a very basic need for any child. In fact, behavioral science tells us that ALL choices, all behaviors in children and adults, are actually strategies to get some need met. If the mom could consider her daughter's actions from that viewpoint, perhaps she'd be able to adjust her schedule, rules, and expectations to meet this angry child's needs. If her needs are met, her anger will more than likely subside.
Few children can accept constant correction and management, even if they 'deserve' it, without distress (nor could most adults). Too much frustration, which the child did not choose to feel, quite logically results in either tantrums or withdrawal. In the case of tantrums or angry behaviors, parents may believe it necessary to add an additional frustrating layer of discipline, which usually translates as "punishment." For a young child, this usually adds to her emotional burden, confoundment, and rage, especially if she has a strong will. Feelings are just as real as fact to the child who's feeling them.
Anyway, I'm assuming you will get the advice we give to this mom friend. So here is my list of the best tips I've learned over my 45 adult years for working with young children:
1. Trust that she is not "trying" to be naughty. Children don't really want to cause problems or get in trouble if they have any other way at all to meet their own growing need for autonomy, independence, and control of their circumstances.
2. Adults have the practice and self-control to make most of life meet our grownup expectations. Your toddler doesn't know any of that yet, and it will be a while before she sees very much from your point of view. As exasperating as that is for you, she can't help it. It's just reality, and reality is easier to take if you can accept it.
3. Digging in heels and tantrums are a natural outcome of becoming more frustrated than the child is able to endure. This "new" behavior may seem to come out of the blue. The stress of travel and changing schedules, or illness, or any major change, may contribute.
4. When she wants something, empathize. Big time, and in the child's language. I love the advice of Dr. Harvey Karp on how to get on a tantruming toddler's wavelength in this and several related videos: http://www.youtube.com/watch?v=G6KnVPUdEgQ&feature=re... . Once your little girl realizes you do care about what she wants, she's more likely to be able to calm down and cooperate with what you need from her. And there are lots of positive ways to approach this, rather than just saying no. They hear no so often, and they can be so frustrated by it. And they learn to tune it out. So look for ways of finding a mutual "yes," as in "Here, play with this," or "Can you hop over to me like a bunny?" instead of "No, don't touch that," or "Stop that and come here right now!" Save "no" for those occasions when children are trying something dangerous.
5. Keep it playful. Children learn primarily through play. You may need help with this if your parents didn't model a lighthearted and cheerful approach when you were little. The book Playful Parenting is a great resource. Your daughter's sense of humor is developing, and you'll both be happier if you can nurture that. (Also be aware that some "behaviors," like throwing, are a natural experimental activity for kids, a form of play that is programmed into them for the purpose of developing brain/body connections. Find plenty of "acceptable" play outlets for those repeating behaviors.)
6. There will also be times when you must have her cooperation, like diapering or trips to the store, so keep a special toy that she gets to play with only at those times or keep her as playfully engaged in the process as possible. This often requires creativity, because each child is different.
7. Here's a big one: give advance notice when you'll want her to be doing anything differently, especially when she's grooving on her activity/play. All children absolutely hate unexpected transitions (and so do most adults). With my grandson, we let him know at least a couple of times that a change is coming ("We're going to go to the store / have lunch / take a nap pretty soon." … and then a second alert one minute before making the change.)
8. Whatever the next activity is, make it sound as desirable as possible. Give some detail about the ride in the car, or a favorite food at lunch, or sweet snuggles before nap. Be positive and enthusiastic. Be calm. Be "as inevitable as the tides." Desperation will show, and even though she's too young to deliberately plan a power struggle, she will quite naturally sense any cracks in your resolve in an attempt to meet her own emotional needs. And this is where future power struggles truly can begin.
9. Try to keep demands low when she's tired, over-managed, hungry, or sick. An already frustrated child doesn't have any emotional reserves left with which to cooperate.
10. Get to know her most likely trouble-spots, and plan ahead. For many kids, it's when they want some tempting object or food they've seen. So keep those things out of sight when possible. Baby-proof your home. Be prepared with a distraction – for example, another toy she likes when you have to take something away from her, or a healthy treat when she wants a sugary snack. Laughter, introducing a new game, a few twirls and bounces, hugs or tickles, a goofy song, can help break into her determination to get something she wants (that short attention span is both a curse and a blessing).
11. Avoid bribes, but let her work toward occasional rewards. Don't try to buy cooperation with "IF you'll do X, we'll let you have Y." Instead, phrase it as if she gets to assist in advancing something good for herself: "Hey, as soon as you help me get X done, then we get to do Y." It sounds like a small distinction, but it's important. It gives the child a chance to cooperate in what feels like choice, even when there's no "if" about it.
12. Be sure she gets lots and lots of physical activity during the day. Time outdoors in nature is calming for most children. If she has pent-up energy, it will have to come out some way, and unless channeled in a positive direction, it will likely to add to both your stress and hers.
13. Whatever you are trying to teach will need to be repeated hundreds of times over the next few years. That's completely normal. Attention spans and impulse control are extremely limited in toddlers. Look at your parenting contract, and you'll find it in tiny print under "I agree to the following terms and sacrifices."
14. Spanking and time-outs don't work for every kid, and will sometimes actually backfire over time. Especially with spanking: children may be scared, shocked, or shamed into cooperating, but behaving for the sake of avoiding pain isn't the same thing as developing an internalized sense of "good." Consistent, calm guidance and demonstrations of what you DO want from her will work better in the long run than punishing for what you DON'T want her to do. See more on this by googling The Science of Parenting or Emotion Coaching.
15. Pay attention to what you love and appreciate about your daughter, and make sure she knows. Remind yourself to do this even when you're tired or busy. Children seek attention and approval, and if she knows you're noticing her good moments, she'll try to create more of them. If she doesn't get that positive notice from you, she'll seek attention in other ways, and that often turns out to be misbehavior, because you notice it.
There's one other thing worth considering: some kids are sensitive to chemical exposures, such as auto exhaust, the scents that fill up the detergent aisle or the modern home, and can feel physically and emotionally miserable if they do get exposed. It may help to make a mental note of when and where these events most often, to determine whether this could be part of the problem.
I wish this mom and her little girl well.