If you trust your vet them I would go by his recommendation of an overnight stay. They might like to monitor afterward and knowing a vet tech is right there seems very reasonable to me. A spay while more invasive than a neuter is still pretty routine as is a dental. It's inexcusable that your cousins dog almost died from a dental! How could her vet not had the reversal drugs available!
The first night after a spay they are still pretty out of it because the drugs are still being metabolized by the liver. But that's not a bad thing since it will help keep her quiet and relaxed. The vet tech can monitor her temperature, check respiration etc and relay any concerns or issues to your vet. Instead of worrying about bringing her home try to take comfort in the fact that she will be well monitored. Personally, I like the idea of the vet wanting an overnight stay
As for the onsie idea don't worry yourself too much. I don't think that a belly and would be comfortable on an incision. Plus the fresh air is good for healing. Just keep an eye on her and limit her jumping. Sounds like you have a great vet and put her care in his hand, follow his directions for aftercare.