Think outside the box on this one. I have a friend who is about 20 years younger than me. I first met her when she was a young teenager, she has now grown into a fabulous, responsible woman.
Should G-d forbid anything happen to me, she gets Tux (my horse) and Remy (my golden). She's never even met Remy, but I have no reluctance with her having him.
Raggedy will go to a dear friend who's buidling does not allow pets of any kind (not even goldfish, it's on the sign!) - but we sneak Raggedy in there whenever I travel and she is happy and comfortable there.
100% of the proceeds of my estate, after paying for my burial and bills, will be put in a trust for the benefit of my animals for as long as they live. The friends who have the actual babies will be able to write checks up to $10K, anything over that will require 2 signatures (between three executors).
No one in my family would take care of my pets in any manner that I find acceptable. The truth is no one anywhere near me would - my friend who would get Tux and Remy lives in Texas - but I know they will be cared for and loved for the remainder of their lives.
I completely understand your stress over this issue. My family does not understand it either - in fact they thing I'm insane. Therefore they have nothing to worry about - I've taken care of it, and made my wishes VERY clear.
Good luck to you, I know you'll figure it out. (BTW I am by no means of an age where I'm expected to drop anytime now - I am 47, but I believe in being prepared)