This sucks for you, but you need to take control of the situation. The landlord will likely not be all that much help and I'm guessing they will advise you to call the police when it comes to middle of the night noise violations. When we rented, we had problems with an upstairs neighbor blasting music in the middle of the night and after I realized how stupid it was to angrily confront some stranger in the middle of the night myself- I started to call the cops.
Call them every time they're outside partying in the middle of the night, every time you hear a fight between the couple and for sure if anything is ever stolen again. Call their non-emergency number, explain the issues politely and calmly and let the dispatcher know you're concerned that problems will increase if the neighbors know it's you complaining. Explain the noise is keeping you and your children awake and you are growing concerned about safety as well. I would also emphasize children being outside late at night as a cause of concern as well. If they are neglecting their child while partying CPS might get involved. I cannot emphasize how polite and respectful you need to continue to be when calling law enforcement, in this case you will come across as the normal, concerned citizen only if you retain your cool.
Be persistent. Landlords will respond to frequent police visits much more than they will ever respond to your complaints. Also, I'm guessing if they are partying, the police will eventually find drugs or some other illegal activity going on. The landlord can legally evict them quite quickly if a felony is committed on their property.
Good Luck. Take care.
I just read through the comments and I'm a little annoyed with the "just move" option frequently expressed. Even if you move and are well rid of the problem, you've certainly done nothing to prevent the next tenant from experiencing the same frustration and grief you're now facing. To fix the problem permanently and to possibly teach a much needed lesson to a couple of rude human beings is a much better solution.