First of all, know that you are NOT alone in this one. Many parents have one child do it right away, and the next one takes forever or vice versa. Children mature at different ages. Don't stress yourself or her over it.
Your daughter sounds like she is a busy, curious child who may not be "body aware" yet. The body gives different signals for stool than urine so she may not have the muscle control to hold it by the time she realizes she has to go. Also, some children's bladders are smaller and need time to catch up with their bodies.
One of the things we did was to put up a time schedule to go every 3-4 hours and a star chart in the bathroom for every time my son went in the toilet. Have her sit on the toilet every time whether she says she has to go or not. It sort of gives the child a chance to figure out what it feels like to "go" and puts their body on a schedule. This works with all ages, even elderly patients, but you have to be diligent and stick with it. If it doesn't work after a few weeks, you may have to back off and restart it in another month.
A call to the pediatrician to make sure she doesn't have a bladder infection or something else going on would be good idea, but I wouldn't use the other kids' development as a yardstick for what your sweet one should be doing, especially her older sibling.
The name calling has to stop completely..you don't want her associating herself with shame or worry that she isn't enough. Try not to show any annoyance with her, especially in front of the other kids, or call attention to the fact that she has wet herself. You can speak to her in private about it, but kids are cruel and have long memories...she may never live that name down. We had a child whose cruel schoolmates called him "wetty teddy" for years beyond elementary...
The diapers at night are a pretty good sign that your daughter's bladder isn't large enough to hold the urine, often also a reason for her wetting during the day. Fluid intake is something to consider for nighttime wetting, although it is hard to tell them they can't drink when they are thirsty.
Lastly, think about the power struggle thing. She may be aware of how much you want her to do it..for ALL of our reasons, and she just won't give in to it. If that's the case, ignore it as much as possible, help her change and get back to what she loves to do, and don't say anything except "we go into the bathroom to pee, honey"..... She won't have any way of "fighting" that...
Hope this helps you...our struggle was a long one too, but once I relaxed, my son did too, and a lot of things beside the potty training came along more easily.... Hugs!!!!