Sorry your going through this. It's hard to go through and emotional.
If her claims of you being abusive are are false then don't worry, as long as you don't have a police record of alcoholic, drug, or physical abuse you'll be fine. Courts understand all of the 'he-said, she-said' stuff - they've heard it all before. The courts just want to be sure that the kids are safe.
As for her getting custodial rights, there's a good chance that she'll be the primary custodian. That's ok, you'll still get to spend a lot of time with the boys. Ask for joint custody and half of the overnights, but know that a lot of dads get around 104 nights per year (every other weekend + one night a week).
Most of the time, even if the boys want to stay with you, the courts won't consider their opinion until they're around 11 or 12 - so they'll probably spend most of their time with their mom. It's probably a good idea that the boys stay together, the 5 year old will really lean on the other two for support.
You can also file an injunction that would prohibit her from moving out of state. Whatever you do, just keep the boys interests first. I hope it works out.


