Animal lovers advice please

So we have two cats and five dogs. I don’t know what my parents were thinking when they got these kittens but we can’t save everyone you know? We have these two kittens that were supposed to be for my younger sister, one is perfectly healthy however the other is a bit different. She was born without a tail and she poops uncontrollably everywhere without even noticing and probably even feeling it. They’ve been to the vet once because my sister is so irresponsible and they don’t even have their shots. They’re about 4-5 months now and they’ve been locked up in a room for their whole life because we have so many dogs that we can’t trust with the babies. We’ve been trying to find a good home but no one wants them. We don’t want to take them to a shelter because they’re so over crowded and we’re scared the only thing is to put the one with no tail and health issues to sleep and focus on finding a good home for the other. We’re really at a loss here, any advice ?