I just commented on your other thread.
I'll say...your problem is not that you want to or feel you need to be able to veto, what you want to control but can't is your partner's ability to be a partner worth trusting. Your stress is multiplied because they've proven untrustworthy, so you feel you need to ask 5x more questions to make sure they aren't leaving something out. Sometimes you catch them at something, so you get even more stressed out and it leads to 50 more questions.
You talk about your partner losing patience with you, but she wasn't patient with your agreements and the boundaries you discussed. I know you say that this post is irrelevant to the other thread but...I don't think so.
My probably unpalatable advice, is that you both stop dating until you work through her lies and figure out her motivations for cheating on you and lying, and deciding what is right and healthy for you. Especially as you feel the pain of her lovely partner who is just trying to be healthy and caring but suffering from the unsettled issues between you and your partner - that's an added burden on top of the other issues you two already have to deal with.
Happiness will never come to those who fail to appreciate what they already have.