can a father with physical custody, but shared custody with the mother...

You MIGHT try contacting http://www.fathersrightsprotectionsystem.com. That organization has been around quite awhile. I'm NOT sure what they can do for you...but I've got male friends with custody/child support issues...and that organization HAS helped them.
Good luck to you and your kids.

Shared, or joint custody refers to who has decision making power. Physical custody refers to who the kids live with. If you have physical custody of your children, she is obligated by law to pay child support to you. If she wants the kids back, she will have to go to court to prove that you are not a good parent and that living with her will benefit them more.

If I were you, I'd apply for a formal custody order that would secure things the way they are, and at the same time, request that child support be awarded. Don't waste time with idle threats between the two of you. Get a lawyer and find out exactly what your rights and responsibilities are and then act on them.

You absolutely have every right to ask for child support. File the docs. Shared legal custody implies that you both have to agree to life changing or legal decisions regarding your children. But the parent with physical custody is entitled to child support. Don't let her scare you from getting what she KNOWS is entitled to your kids. Be prepared to prove you provide a stable environment for them and that she is unstable and irregular in her contact with them.