Is there any way you can possibly make the marriage work?
You are about to totally complicate your life and God knows what it will do to your children. I know sometimes, such as when physical abuse is involved, we do have to get out. But, short of that, I say stay married.
If he has cheated on you, if you have a boyfriend (or girlfriend or whatever - not my business, don't want to know, just trying to cover all the bases), whatever is going on, decide to forgive and stay together.
Divorce is generally not a real good answer. You don't want a judge ruling your life and that is just what you'll get if you involve the courts and lawyers. You also stand to lose custody altogether and might even be ordered to pay support to him if you make more money than he does. Also, Social Workers might come poking around and who needs that?
I think you are maybe feeling your oats because you are done with school and you think you want to start fresh and throw out the old, bring in the new. Don't do it, is my advice. Take a breather, let the world spin a little bit, just keep your feet on the ground. You presumably made vows before God so now honor them. Ask Him for wisdom and strength to do so and He will honor you for honoring Him.
Unless there is really, really, really a totally valid need to divorce, like you or your children are being battered/raped, stay married.
Just another thought: If you move with the kids before any divorce or separation proceedings begin, that is perfectly legal, as far as I know. But, of course, your husband might not take kindly to that and could retaliate heavily. Maybe you'd be ordered to get the kids back to where they are now. I don't know. Of course, you need a lawyer. I still say stay together and work it out. Close any joint accounts before he can, if you really mean to leave.
I guess you and your partner have discussed this and there's no possibility of a peaceful parting? He might be relieved that you want to leave and glad to no longer have to support the kids.
Have you considered what being a single, full-time working parent will be like? You can't really count on your aging parents all that much, I'm guessing, as they probably have some health issues. But maybe there are other relatives and old friends - or you'll make new ones - who can help you.