I don't quite get what you're saying here, you're saying you're all Canadian and you live in the US and you're awaiting LPR status? And you're on TD or H-4?
Whether or not you can successfully leave and re-enter depends on where he is in the application process, although as he is the person applying for AOS and you're just listed as dependents it's not such a big deal as you have valid non-immigrant status. The main problem would be if you leave and he completes AOS while you're in Canada, then your non-immigrant status would no longer be valid, although it would be possible to obtain immigrant visas in that situation if you're listed on the G-325A.
If you're planning on living in Canada there is little point in obtaining LPR status in the US because if you spend more than a year outside the US you lose it anyway. And you can't file
taxes as a Canadian resident either, if you do that you also lose it.
If you're filing for divorce then you are no longer a dependent and don't qualify for LPR status.
As for your children, the custody situation is much the same regardless of which side of the border you live on, you have to agree custody and if you can't you have to go to a family court who will sort it out. If you cross the border in this situation you need the permission of the father to move the residency of the children (as you would if you were say, moving to another State), best to get it in writing with his contact details. The difference is of course is that the border people may check.
Steve.