>If I took his offer and not theirs they would see it as me cutting them out and as a betrayal.
If this is the sort of language they used then I would run from these people as fast as I could. Don't let anyone emotionally blackmail you into doing something you don't want to do. If this is how they're acting now imagine how bad it would be if they were actually your business partners and had actual rights as share holders of the business?
>I’m sick to my stomach over it. I can’t get rid of them. I can’t negotiate.
Try to remember that you have no obligation to even speak to these people.
Also, please get yourself a good lawyer before you sign anything with anyone; and especially don't sign anything that people are "strong arming" you into signing.
>The only hope I have (in my mind) is if I can raise a round in the next year and have them bought out. I don’t see any other way.
You can just politely tell them "no thank you, I'm not interested anymore."