I'm no expert, definitely new myself...
Is it possible to work out a relationship that you are both comfortable with. Not either she dates multiples while you only date her or you two just date each other... Would you feel better if you both dated someone else?
I know that can be tricky (especially with genders, we can't help what we're attracted to), but maybe it would be easier if you felt attracted to someone she did as well?
That's the only thing I'm comfortable with in my relationship... I wouldn't be okay with my husband dating someone that I wasn't also involved with. That's just where my boundary is and he agrees.
I'm sure someone with more experience will be in this thread soon to help.