If you have not promised exclusivity, don't promise it NOW just because she's inclined to pressure you toward that expectation.
Remind her point blank -- "Remember I have not promised you exclusive. If this has become a dealbreaker for you please tell me now. I cannot be a mind reader"
And then go date when you want to. If she's over too much tell her so.
"I love you. I will see you on __(whatever days are her days with you)___. I need space to myself to rest, and I also need space to myself to date. I am willing to help you manage your jealous. I am not willing to stop living my life because of your jealous. Talk to me. But I need my other times to myself."
Let her own her feelings. Perhaps read this article together and she can do more page 5 and you do page 6.
AND continue to date other people. It's never going to "become the new normal" if you are not dating others like you want to be and she opens herself to learning to cope with it. She cannot rise to the ocassion if it never actually comes up for her to deal with. YKWIM?
You are not doing this to kill her, and seriously? Going out on a movie date with someone else and chatting, and maybe a smooch goodnight on the mouth? Apart from the kiss you could do that with your nephew. You Dad. Your sister.
She signed up to be in polyship with you, not monoship. If monoship is now what she wants, she can inform you. You can ASK her if this is now what she wants if you are getting that vibe so you can have the verify/clarify.
And then you both can end the romance part and choose to learn how to continue on being good exes and friends. Because you want to be in a polyship. Things do not match up in the romance department.
If she still wants to be in polyship with you, she needs to be realistic about what it takes and willing do the work required. Including working on her emotional management.