How do I search for dog sitters that are good with rescue dogs?

Rather than boarding, I suggest that you hire someone to stay at your home. That is much much better for a dog with SA.

New: I wasn't sure what you meant by casita since that only means a small house to me, so I did some Googling. It sounds like what we call a coach house, a separate unit on the property of another, larger house. Regardless, if you are able to have someone stay over, it is far better for the dog to stay in her own surroundings. It is bad enough that you won't be there, but to be thrust into an alien place could drive the dog to do destructive things to either the sitter's home or itself. SA dogs have been known to chew on doors, walls, etc., to try to get out and get home.

I tried to sit for a neighbor's dog, who we knew well and played with my dog. He always comes up to me outside for a treat. But in my home, he climbed up onto the furniture to look out the window (2nd floor) and I was afraid he might try to break the glass or chew/scratch on the front door. He's been on medication, like doggie Valium. We tried acclimating him to staying with me, with the owner dropping him off and picking him up again a couple of hours later. That still didn't help. Finally, they hired someone to stay at their home and that worked. He knows his surroundings and must realize that his humans will come back. They've had to do this for years now.

So I can't emphasize enough how not subjecting the dog and a sitter to that condition is. You might also talk to your vet about giving the dog some Benedryl (the amount depends on your dog's weight); it helps calm them and make them sleepy.

There definitely are some sitters on Rover who have experience with separation anxiety and rescue dogs. There are also sitters who do not have much experience in these areas.

I wish that there were filters to help with this type of search, but there are not. My suggestion would be to closely read profiles to determine which sitters may be a match, and in the rover messages, you can let them know of her Sep.Anx. & ask if that would be a match for them. For a dog with Sep.Anx., I’d only contact those whose profiles indicate they stay at home (not working outside the home, going to classes outside the home, shuttling little kids around, not walking other people’s dogs, etc.) Depending on the level of SA, If you can find a sitter who has considerable experience and someone responsible stays with the pet during entire stay, boarding may work out. It’s likely these sitter will be mid-priced or at the upper-end of the competitive market. My dog has dog friends who had experienced varying amounts of SA elsewhere - home alone or other locations - & are perfectly happy staying with us /some don’t even care to say bye to their human owners)