What happens if I refuse to send in financial statements to Child Support Agency? Should I fight for custody?

We divorced in 2001 in the divorce it stated that whoever left the county first, lost custody, she left first, I did not fight that. She has also met others on line and moved to different states. I was not court ordered to pay child support. Now I live in a different state, I pay insurance, buy their clothing, and also let her claim both kids on income taxes to let her have the money although I legally should claim one, and about 6 months out of the year I give her $300 a month. Now she is going through the child support office to make me pay child support, what would happen if I did not send in my financial statement to the GA child support officials? Also her housing conditions are not the best, her floor is sinking in and other issues. SHould I fight for custody for their best interest?