Whether he is cheating or not this man is behaving inappropriately. Sometimes we make excuses to ourselves so that we can feel better about our decision to accept less than we are worth. You are on a camping trip with him, you are his fiance why is he spending all his time with another woman. Even though you expressed ur discomfort he still refused to stop what he is doing, I heard a saying "if you have someone in ur life and you tell them u r hurt by their actions and they try to change then that is someone to have around but if you tell someone their actions hurt you and they don't stop they do not deserve to be in your life." He is being disrespectful.
Whether you decide to stay or leave is up to you and noone can judge you for either, but I am here to tell you to know ur value and know what u r worth, do not settle for less than u r worth, no man is worth that no matter how much you love them. He is acting like a silly love struck teenager, if when he speaks of this woman it is not something pertaining to the children it is not relevant.
The only reason he's not with her is because he doesn't want to cause a family rift - he's told you that right out.
I don't think I'd be with a man who really wanted to be with another woman, but there was just an impediment (and not really a big one, my guess is they will be together eventually) that was keeping him from having who he really wanted.
Just my humble opinion. They both seem to really want to be together.
whilst i dont think he is cheating on you this is obviosly making you feel uncomfortable,i get a man can find another woman interesting and pretty and can always look at the menu as long as they dont order,but to spend every minute with this woman on your vacation is a bit much,speak to him and tell him that this made you feel jealous and upset,dont just walk out that solves nothing,you have obviously been hurt in the past and your insecurities could be getting the better of you,some men are just very friendly and lovable people,so please dont assume that he must be cheating,you obviously fell in love with him for his sweet kind loving ways,so please speak to him honestly about how you are feeling,but i honestly think this is more your issue than his,i really hope you can come through this and be happy