When it comes to most things, at least the big stuff, I think my wife and I agree on how we want to raise our kids. Ours are age 3 and 2 now. Whenever we don't however, we seem to find a common ground and we both agree on the rules and a parenting style. The problem is that I still see my kids doing things we agreed they wouldn't do but not because my wife let's them, it is because she doesn't see them. for example, we agreed no sharing food with kids who are not close friends at the park but the other day I arrive and the 1st thing I see is some strange girl sharing her food with her. What should I do about this if it happens all the time. I get upset with her but maybe I shouldn't because she doesn't do it on purpose she just is less of a control freak than I. Must I just back off and accept that she is going to be less vigilent and more relaxed than I and see less of the things we are trying to avoid our kids doing? Or should I insist that she get her act together and stick to our agreement? I make a great effort to teach my kids so if they get to do these things in her care, it seems like a waste of effort.
Taking all that you've said in your question and the following comments, to my understanding this is what it boils down to (correct me if I'm wrong):
As the parents, you agree in principle about something. In reality, it's not that she doesn't see them, it's that she is for some reason incapable of follow-through with what she agreed on in principle with you. This then is frustrating for you, because you're acting on the principle and she's not, which you think is (unfair/dishonest/you-fill-in-the-blank(s).)
So there are three problems, over which you have limited control or influence.
"You agree in principle..." If she doesn't follow through, she may not actually believe in what you agreed on, but is merely saying she agrees. You have no control over this at all. You can ask her to be more honest and forthright about this so you can adjust your expectations accordingly ("Whenever we don't however, we seem to find a common ground and we both agree on the rules and a parenting style"), but if she won't, she won't.
She can't follow through. That's either because she doesn't see the value of it, or some other deeper reason (she's too tired, she doesn't want the child to make a scene which would be embarrassing, etc.) You have no control over this at all; she has to deal with this. Maybe by getting more sleep, maybe by hiring a sitter for a couple of hours a few times per week, maybe by realistically evaluating what she can and can't do without giving up on a given day), maybe by reading a good parenting book or some good articles online, etc.
You feel frustrated/wronged/frightened-because-her-actions-are-hurting-the-children/disrespected/other (you need to fill in the blank) by her failure to keep up her end of the parenting agreement. Your feelings, unfortunately, are your problem to take care of, because you can't change her behavior. Only she can do that. If you protest, "But I wouldn't feel this way if she only kept her promise!", then you're expecting her to fix your feelings by changing her behavior, which rarely works in real life. This is the problem you have the most control over.
what to do when parents agree on parenting but one can't stick to agreement?
Figure out what the real problems are, and work on them. Face them honestly together, and figure out how to change your respective roles in the creation of the problem(s), accepting that one human being can't control another (true for better or for worse.)