Respecting the relationship?

So I have been dating this girl off and on for almost 2 years now. Any time she goes out either she won't tell me where she is going or what she is going to do. Mind you at one point she lied about a guy picking her up and slept with him even though we were fighting about whether we were going to continue so she justified it as we were separated and she needed to feel like she really needed me after that. So forward to now, she will just up and leave and say something to the kids but not me. So if you saw this type of behavior In a partner (male or female), would you want to continue with this person?
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Yes we are in a serious relationship however she keeps insisting that it's ok for her to go see her guy friends all of whom are single and we do live together. We moved in a meer few weeks into the relationship.
Respecting the relationship?
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