A 10 year old and a 4 year old are going to make a ruckus. Banging on the ceiling with a broom is an open invitation to kids of this age to bang back. There is no way that they are going to quiet down from that, it seems more like a game than an admonishment. If Mom heard the banging, she might take it wrong and think your being rude or weird. Also, that isn't going to be calming to either you or your husband.
You have options, but whether they work or not is really up to how tolerant you are and how much Mom upstairs is in control. You will have to tolerate some level of noise.
1. If you are somewhat friendly with the neighbor, ask her if your husband can walk and stomp a little on the floor upstairs and see how loud it is. You might find out that the noise is louder in your apartment than it is upstairs. This makes it really hard to be quiet.
2. Talk to her again. Let her know how much it bothers you without sounding insulting to her or her children. Let her know if there is a specific time that you would really appreciate a little more quiet.
3. If things don't improve, be a bug. Go annoy her by knocking on her door and asking her to quiet down or calling her on the phone. If this doesn't work or makes her unfriendly, it's time to call the landlord.
4. Call the landlord. Explain the problem. Ask him to intervene or add some soundproofing in the ceiling or carpets upstairs. Maybe the 2 of you can trade apartments?
I really don't think that calling the cops will work. It will instantly ruin the dialog and relationship with your neighbor. Use this as a last resort and they won't take you very serious unless it is crazy loud late at night. I think it will make your wait to move even more miserable.
I don't know what the climate is like where you are, but it is freezing here and my kids are going bananas. My upstairs sounds like a herd of buffalo in a cage match with a troop of gorrillas. I try to control it, I mostly succeed, but there is no doubt that everyone will feel better once we start spending some more time outside. (then you can look forward to screaming children that scare you because it sounds like they're being killed...that is my huge pet peeve. NO PLAY SCREAMING! IT'S SCARY!)
Good luck. Take this as a good parenting lesson. Someday you will be on the other side of this equation, no matter how good your child is. You will find out what it's like to have your children bother somebody. It is embarrassing and frustrating. When your embarrassed, you don't act right sometimes.