Well, what were the terms of this agreement? Were they still your goats and they were simply holding on to them for you? Or did you literally GIVE the goats away, therefore making the goats the other family's property?
I'm sorry your favorite goat died, but if you gave them away then they're no longer your responsibility.
I'm confused as to why they'd offter to give you back a kid and the other goat when you stated you couldn't handle the 2 goats you had before. Has something else changed? Is Lilly's death their fault - meaning they refused to feed her or injured her in some way? If it "just happened" it could have "just happened" for many reasons, including the stress of moving to a new home.
If I "gave" the goats to someone with the condition that the goats would return to me at some predetermined time, then I would accept the kid and other goat back at that predetermined time.
If I GAVE UP the goats to someone and now the goats are solely their responsibilty, morn her loss and that's about all you can do.
If you can give the kid and Lilly's sister a better home than you could before you gave your goats away, great - take them and move forward. If not, I'm sorry to say there's little you can do but cut your losses.
It's true that some people may 'care' more than others about goats, but just because she died does not mean these people aren't good caretakers based on the little information we have.
And FWIW, I've been given free goats and I've paid over $200 for 1 goat. There's no difference to me where they came from - once they step into my car/on my property their mine and I can do what I wish with them be it give them away to someone else or sell/keep them. I've promised one of the people who gave me 2 registered goats for free that I'd take good care of them and give them a good home. If they happen to die at some point soon (I've only had them for 2 months) then it is what it is. I sure wouldn't offer them a kid and the other goat back, though - they were given to me without the condition they'd return to their former home someday.