No. You better not take the children away without permission while your divorce case is in process. This will make you in the worst situation possible in court.
Yes. You can have physical custody of your child perhaps two children. This depends on your agreement with your wife,letting her know the plus and minus marrying an American guy with two step children. And depends on how you two get to this stage. In the worst case, you can always seek for legal help.
I wonder how the American guys are any better. Time has changed, what I can say.