Ugh. That's a very tough situation, and I am sorry your mom is having to make such a tough choice. I hope that both she and her gf can come to a place where they are both at peace with things.
Anyway, I would just say, "Grandma is going to take care of your cousins for a while because their mom is sick and can't take care of them right now. Taking care of 3 little kids is a big job and Grandma will need to be focused on them because it will be hard for them to be away from their mommy. So, Grandma's friend is going to live in her own apartment for a while."
If you are uncertain whether or not your mom's gf is going to keep in touch with you and your DD, that's all I would say for now. If DD asks, you'll have to be honest and say that both grandma and her friend are a little stressed out over the situation right now, and that you'll have to wait until things settle down.
If, on the other hand, you are reasonably sure that mom's gf will keep in touch with you, you can add, "We will still see Grandma's friend sometimes, but she and Grandma won't be living together."