Since my father is a veteran, can he get help with a funeral trust that Medicaid can not touch?

On talking to staff member at the nursing home, she suggested getting a funeral trust to get it under $2,000. What's the best way to go about getting a trust? We will reapply after his bank balance. The way I understand it is, we can do this even though we filed for Medicaid because we were rejected and have to reapply. That is legal isn't it?
He is in rehab and doesn't plan on staying there long-term. We plan on getting him an apartment and using CICOA services after he is out of the home.