Any advice on how to move on?

Posted it in detail in various places, here is the digest: I am 45, my wife of 18 years told me she no longer loves me and wants to move in with her new bf in India. We have two boys 16 and 13 and I am looking at being a single dad within a few months. My wife still lives here and seeing her every day is hell. I used to have strong feelings for her, but those are fading and it makes me sad and depressed. I'm in fear of what is going to come and how I can give my boys a good start into their lives with them having their own issues (older one has gender identity issue, younger one says he is gay). The older one finished high school and is off to college while staying at home, the younger one wants to continue homeschooling. My wife says that he can be half a year with her and then half a year with me. I have no clue how a 13 year old can even manage the travel, let alone being thrown into a totally new world and then ripped out of it half a year later to go back to the place where all the pain started.

I so desperately want to meet someone right now, just to talk and be together with. 7 cups is help, but I feel as if I need something that is more personal and up close.

I need help and advice. Advice on what I should do with my youngest son. Should I go along with him travelling the globe alone or should I suggest that if my wife wants to do the schooling to do so via video chat? I thought about sending him to public school, but I know he won't last there and he may feel as if now his dad is sending him away as well. I'm worried about my oldest son, who yells at me "I'm fine!" when I ask how he is doing. He is so angry at his mom that she plans to pack up and leave. How can I tell him that times will get better? I so desperately need some warmth and a real hug that means something, but I have no idea where to meet someone. Tried dating sites, they all suck. Went to a local singles outreach, they are all 60 and over. Had one idea of making a nice sign that says "Do you want to meet me and find out what might happen?" and stand in the busiest place in the region. I bet it gets me on the 6 o'clock news, but I doubt that is the attention I am looking for. So how the heck does a 45 year old meet women who might be interested in a serious relationship? Should I just ask any women I find attractive if I can take her out for a coffee? With my luck I get beaten up by her boyfriend.

Any tips on how to get a grip on the future and start over with a new relationship?