How can I stop these neighbors below me??? (kinda lengthy)?

We had moved into our apartment complex in January 2010 and everything was great for the first 2-3 weeks or so. Me and my husband got into a fight one night and the lady who lives below us come up to our door banging and screaming obscenities to us telling us to shut the "f" up and what not. We did apologize to her because we understood that we were a bit loud. We didn't understand why she had to be so rude. That little incident was that START of everything. We live in an apartment where the floors creak when you step on them, they aren't well built anymore. we were walking in our apartment taking care of our little boy who was maybe 4 months old was was born 2 months premature. There was no noise in our apartment as my husband was asleep and I was taking care of my little one trying to get him a bottle and everything. Suddenly the lady again, walks up to our apartment, bangs on our door, screaming obscenities. We opened the door and she says that "our" walking is scaring her kids and she wanted us to walk "lighter" Now I have no idea how to walk "lighter" and us walking is scaring her kids is pretty damn crazy. They should EXPECT to hear people walking above them as it is an APARTMENT complex!!!!! I mean during the day, all day them slam their doors like crazy and play their music loud but do we complain to them and be rude about it? NO! It's not like we purposely STOMP around our apartment every time we walk!!! So we just ignored it and went on thinking this madness would stop. But no...Now they would bang on their ceiling very loudly every time the floor would creak or something. Our son had suddenly gotten a virus called RSV which is common in premature infants we were in and out of the hospital a couple times and it was stressful for us. They had him put on a breathing type machine that would give him medication through a breathing mask and the machine was quite loud. But for the health of our little one we could not help this. Now every time we turned on the machine to give him medication they would start their banging. One day we had to call 911 for an emergency with our son, and a big fire truck was in front of our apartment. 5 firemen came up and was examining him and of course the neighbors banged through the whole ordeal... We had had quite enough of it so we called security explain what was going on. They told them that we were "vacuuming at night" When it was our son's machine. We told the security about our son and his health, but we were told just to ignore the neighbors banging. So really the management won't do anything about this.He had told me the lady was so rude to us because she is "bipolar" My husband is bipolar as well but he doesn't go cursing at everything he sees like she did!!!! So we had ignored their constant banging for a while. Because of all this banging we have to keep our dogs in a KENNEL all the time just because we don't want to put up with their crap. The lady came up once more and this time it was because my dog was walking around. "WALKING"...So I cursed her out and told her what a child she was and she has not come back up here since. Now I know I shouldn't have done that but I was at my last straw with these people....If we drop something on the floor, they bang, if we talk too loudly they bang, If we are not even doing ANYTHING, they will bang. Sometimes even why my son is crying they will bang. When we get into bed at night, our bed makes a little bang noise because it is broken, they will bang as well! WE really want to move to another apartment in the complex but we just don't have the money to do so....We really don't know what to do about this situation and we are so sick and tired of it... We really can't live this way, they complain about us EVEN DURING THE DAY. We want to move but we just can't afford it... What can I do about these people? How could I file harment charges in ARizona?