After seperation wife tells me there is a chance she'll come back and an hour later I catch her with her guy

My wife and I split up recently about two weeks ago, I found out she had been seeing another man. She moved out to the same Motel where "dude" lives at and worked across the road. She tells me that she wants me to work on some personal problems and then she might come back. I had a good conversation with her on the phone about us both trying to work things out and rekindling what we had and she seemed very genuine about it. Exactly an hour later, Im in town getting my haircut and who do I drive by? My wife, son, and her "dude" driving about town running errands. What should I do? Cut off all hope in trying to make things work or continue see trying to get her back? I love her but I dont know if I can keep dealing with this.