I am in a similar situation to your love. I am married and have a boyfriend. With much negotiation we have agreed that I will not be with other men sexually. It took a lot of talking and a lot of rearranging our lives, but it works for us and I am happy.
There is no reason why you have to suck it up and pretend that you are okay and will be happy. I would think that will eventually eat your heart out and make you miserable. If this man has decided he loves you then I think I would ask him to establish with you what the boundaries to your relationship would be. That is totally reasonable. It sounds like you require that he contact you when he is in the city and that he see you. It also sounds like he needs to start being honest about who he is seeing. Perhaps you could even request that he stop adding lovers to his life as he is getting short of time enough to establish and maintain fulfilling and connected relationships. There might be more you would ask of him that you would add.
People who love each other show it by doing their best to help those they love get their needs met. This relationship is not an affair like the one you had for 10 years. This one is structured so that you can enjoy some time with this man and legitimately ask for some of your needs to be met. It doesn't sound like he is willing and able to meet all of them so you will have to decide if it is worth working on... starting with communicating about some stuff seems like a great place to start and see if you and he are up to it. Meeting his wife is a really good first step also.