All kids can be difficult. Usually with kids it's when there aren't rules our boundaries in the household - kids like those. It gives them comfort to know that they can't get out of control and that someone is in charge.
Spankings tend to make kids feel like things are out of control, so I wouldn't recommend that. Nothing makes mom seem more like she's lost it than if she hits her kid. Just my thought, but I know when I've wanted to ... I've been at my wits end. So better to have rules/consequences in place than to let it get that far. I get that you are frustrated.
What works for me and my kids was to not allow them to join in our family fun if they misbehaved. Nothing speaks to a kid more than to be left out. Not in a cruel way - but if mine were not sharing or were just being nasty to another sibling or weren't cooperating (and this is after you make sure they are well rested, well and well fed) - they were not invited to play whatever fun game I was playing with other kids.
If I had a child who was being disrespectful - well, they were separated until they could apologize and come and join us in a calm kind way.
Not as a time out really. If a child just needed a moment to collect themselves (I have one who frequently needed this) they were told to go to their room. They could read or play quietly - it wasn't punishment, and they could rejoin us when they were ready to be civilized :)
With screaming toddlers, I would just pick the baby up and move to another room and say "We don't really like hearing you yell so when you can use your quiet voice, you can come play with us". Stuff like that.
My mom did this with us, she did it as Kindergarten teacher for years, and it works. You have to be consistent.
Good luck :)