awww, I know how you feel. Gracie Ruth had to stay overnight too and I really wasn't ready to be a whole night without her. However, I knew if there was any complications I would want her right there for immediate treatment. He'll be sleeping most of the time anyway and actually probably won't miss you much.
Horrors, I know, but it's us that miss them more during this time.
Prayers for Baxter to have an extra special easy time, and for you too!