Giving up your dog because they elderly is such a shitty thing to do. You're going to abandon them and put them into an unfamiliar environment when they are on the decline? It's even worse that you are assuming they'll be put down anways. Take some fucking responsibility.

If you can't handle the full responsibility of a pet you shouldn't have any imo. That includes making hard choices later in their life. Maybe you should surrender your other dog too since that seems to be what's in their future anways.