Yes I'd trap the final kitten otherwise he will die out there alone. The kittens maybe ok, I don't know much about Feline Aids. They may not live as long as non infected cats but I am sure they can live an ok life but I think they have to be kept indoors only so they do not spread the illness to other cats. Sorry Mum and to be PTS but I think it's for the best for the poor cat.

Good luck catching the final kitten and I hope they'll all be ok.