Rain, I think you are totally in the right and have every right to do what you plan. It's YOUR child.
Infortunately, your mom is ignorant about how wonderful a gay man can be as a friend. Being gay doesn't mean that he's anything else, like a pervert.
I had a wonderful gay friend. He loved my youngest and would take him to his house to give him a treat and bring him right back out. My daughter, of all people, used to have hissy fits when I allowed it. She thought Neil might "molest the baby." Give me a break! Just because he was gay, didn't make him a pedophile!
Neil was one of my best friends until he passed a couple years ago... and no, it wasn't from HIV.

And Neil's "Johnny" isn't gay!
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Psalm 119:105 Thy word is a lamp unto my feet, and a light unto my path.