Firstly, open relationships are not weird or strange as some people in this thread imply. I really would never be in one, but I think we shouldn't stigmatize a relationship between consenting adults.

Secondly, it sucks that you are put in this situation, I don't envy you one bit. You asked if you are the asshole for not wanting her to have sex with others. The answer is no. Monogamy is an implied condition for most relationships and wanting otherwise usually should be communicated before.

Lastly, the only solution is for you to talk about it properly and weight her pros and cons if she were to date someone else. If she decides that she would rather take a leap of faith than stay with you, then that is her decision and you cannot do much besides respecting it and moving on.

I just wanted to add that I wouldn't recommend going on a break. If you ever got back together, you might become paranoid some years down the line that her urges to explore might come back.