I would suggest keeping her in the same room or space as you with the door closed if possible. Just for that extra barrier for sound and a "safer" space. If you're already doing that, then perhaps keep a bag of treats on hand and call her attention and give her a treat to distract her. You can't really control the barking per se, you can over time control her reaction to it. The sound is making her anxious and vigilant instead of allowing her to rest and she's responding to it. Try that out and see how it works. My pup was like that for a while when I first got her too, after some time and her sleeping in my bed she just finally stopped unless it was super loud or closer by. Unfortunately, you just can't stop the sound that someone else is making. Good luck!

I would 100% recommend contacting Rover about it. It's too precarious of a situation to keep your cat and their dog in the same, unsafe environment. It would be easier for either of them to be injured by the other. Contact them and contact the owner as well and let them know it's not working out.