My husband cheated on me while I was pregnant and the mistress got pregnant too. I ended my pregnancy with complications and it was terminated. She now receives child support and I am filing for divorce and alimony. Can I go after her child support since I have proof she knew he was a married man?

No

You don't have any children to support. You might get alimony but since he is paying child support, you may not get as much as you hope for.