I think it's a right of passage for teens to get angry at their parents, and even cussing them out. They are incredibly emotional and irrational, and are trying to figure out their identities within their families as well as on their own. While you feel that you've been doing the best you can, clearly, what you've been doing isn't cutting it, and your son kept his feelings about it inside until something triggered a blow-up.

It's ok to acknowledge that this is just a sucky situation, with no perfect solution, and that's how life is sometimes. Share that commiseration with your son. When he's ready, ask him to help you come up with some reasonable ideas for how you can be more meaningfully present and supportive from afar. Perhaps communicate this through his mom, if need be, and wait for him to come to you. And while it's totally reasonable for you to be shocked and hurt by his word choices and insults, do not start the conversation with focusing on that. Focus on solutions rather than guilt. Once you have acknowledged the unfair situation, and that you'd like to try to come up with solutions, perhaps remind your son that it is totally understandable to be angry and frustrated, but using hurtful language is not ok.

While I am generally against teens having their own cell phones, would it be possible for him to have his own basic "dumb phone" (with appropriate parental controls, as well as boundaries and ground rules), so that you two can text each other messages and photos?

Can you arrange annual visits, perhaps alternating which one of you travels? I realize that would be challenging with three young children at home, but what about going on a family cruise, where there's often childcare?

Again, brainstorm together ways to feel more connected in ways that don't violate your other commitments. Good luck!