A friend of mine gave away a dog a few years ago - problems at the time made it the best solution - and insisted on meeting the whole family and seeing the house; she was good with it but made them promise that if ever they couldn't keep the dog they would let her know and she would take the dog back. Two years later she got that call, and was in a better situation so could take Butter back.
If you don't mind keeping the goat, it does sound wonderful for the daughter. If mom does get a place, maybe you could put the same conditions my friend did on the deal - if she can't take care of the goat, bring it back to you.
I will probably do that.
You say she is moving in May, so how can you do this? Unless you travel to another state or area where she is living you won't be able to do so.
My feeling is this:
While I understand and appreciate your feelings for her child, you have a responsibility and obligation to place the goat in a safe and good home. In fact, when I first started reading your original post I thought you did not want her to have the goat since you don't really trust her, and were looking for advise about how to let her down easy.
Maybe you can put her in touch with people who sell goats where she is going to live and they can do the inspecting and so forth to make sure their goat is going to a good home.
I also have to ask...are we really talking about a goat, here, or is that a code name for something else? That happens so often on here that I'm kind of worried that I'm talking about goats, or some other substitute thing, and everyone else knows it's really a blue 1973 Toyota with a Merle Haggard neckerchief in the glove compartment.