I have 2 adopted children. I am divorced and paying child support. My exwife receives a monthly payment from the government for these 2 children. Should this amount be factored into my monthly child support payments

What state are you in? It mat have an impact in how much money is being made for her household and that is what will set the base for support.

Why is she receiving state money? Because of her low income? Because of a disability? It all makes a difference.

But being adopted does not make a difference. Once adopted they are your children.