Gross!
My husband's parents have a disgusting house too. They have four large dogs and two cats in one three-bedroom home. You walk into their house and you get hit with this AWFUL smell immediately. There is animal hair covering EVERYTHING. Every time I go in there, I have to take a shower when I leave.
IMO, just tell her the reason you don't want to go. That's exactly what we did to my in-laws. They are absolutely welcome at our house any time, but I do not and will not subject my kids to that disgusting environment. We told them that, and they refused to get rid of any of the animals, and we just said "Oh, how sad, you chose the animals over having your grandchildren visit you."
I would just tell your friend-- "You can come see me ANY time, but your house has too many animals and I don't want my baby crawling around in there. I will send a gift, I love you, and see you soon!"