You are her Mom and you know her best and know her condition best.
If there is no other solution, besides making her go with you all, then she needs to go.
Or, what if this then leads to her purposely making everyone miserable every time she does not want to do something, as a FAMILY??? She knows you must all fear her acting out & being Bi-Polar, if she decides to be that way.
So you give in or not.
Yes she is 18... but as you describe, she is not responsible enough to be alone. And what if something happens to the house? And you will be responsible for that.
Or, you have someone, a relative, stay in your home WITH her, with rules and that's that. Making sure she takes her medication or not. Not her staying home alone. Certainly if she has never stayed home alone for any length of time... and PROVED that she can care for herself and the home.
And what if something happens, if she is home alone... and it involves the house or a neighbor or etc.? You will be liable for that.
She does not sound like she can responsibly care for herself or the home, if alone. As you describe it, and per her condition.
This is a family vacation, right? Well, when I was that age, and we had a family vacation, we ALL went. There was no choice in the matter. It was a FAMILY event. Otherwise, only my parents should have gone on a trip themselves.
all the best,