For the last few months, we have been preparing for my husband to be laid off.. so in January we gave our dog to a new home. We felt keeping her would make it tougher if we had to just pick up and move.. especially into an apartment!
Our daughter was 3 1/2.
We told her that it was time for our dog to spread some more love to a new family. The woman she was going to needed our dog to love her, too. We explained that our dog would be very happy and get all the love she needed.
We brought our daughter with us to bring the dog to her new home so she could see her new home and all the room she'd have to run. It was good closure- and my daughter didn't cry once. In fact, she tried to soothe the dog.. "It's ok, you'll be very happy here! I love you!".
Sure my dd asked when asked when she was going to a new home, too, but we'd just say, "Never. People don't give their children to new homes. Sometimes just pets. Mary just needed a special dog to love her. Brownie is just that special kind of dog."
See if the rescue mission will allow you to bring the cat to a neutral place so your child can see where the cat is going.. it'll put closure on it for her and she'll be able to visualize the cat being in a happy place.
Hope this helps!
M.