I really feel for you, what a shame. I suppose you have to do what's best for Mack, but that doesn't make it any easier on you.
I lost my boy when he was only 9 - a freak accident in the field which resulted in a fractured pedal bone that never healed. I was utterly devastated and although 4 years ago and the pain has dulled, it never goes away.
I know Mack's not being PTS but having to give him up will be just as traumatic. I really feel for you and your sis but at least you know if someone else takes him on he'll get the care he needs which will ease your conscience.
I can't think of anything else to say, just that I'm thinking of you and hope you get the situation sorted as best you can. Perhaps after a while you'll get another, perhaps not. I always swore I wouldn't, but I am getting another one soon. I miss it too much.