Can you get an air embolism if you douche while sitting in the tub and if you squeeze air into the vagina trying to empty the douche container?

No: No, you will just get some air in the vagina, which will then come out.

Highly unlikely…: While air embolisms can occur from introduction of air into the vagina, it requires that the air be introduced under sufficient pressure to enter into the vasculature. Usually this means the air got into the uterus at a time when the vasculature of the uterus was exposed enough to allow this to happen. It would be highly unlikely to get a significant air embolism from the method described.