Hugs, sounds like a really tough one for you to be dealing with day in and day out.
A really helpful perspective that someone once gave me was that toddlers have very little control over what goes on in their lives. What goes in and what comes out are pretty much it, so it's not surprising those are perhaps the two biggest battle grounds for us as parents. What I would suggest is to try your utmost to make it a non-issue. I don't know if you've come across the division of responsibility model, but to paraphrase horribly it's basically your job is to provide access to a healthy nutritionally balanced diet, his job is to eat it. You can't do his job for him, so it's almost about relaxing into your side of the bargain and accepting that he will, or won't, stick to his side. Kids will not willingly starve themselves if all else is well (I'm assuming here that there are no other issues, medically or developmentally that could be playing a role).
I don't think his milk intake sounds excessive for his age, though probably wouldn't offer more than that. I would probably decide on some rules and stick to them regardless of tantrums, screaming or refusal. My suggestions would be that everyone eats together at the table, food doesn't happen anywhere else (for now). He's two, he doesn't get to 'refuse' to sit with you! Food happens at meal times or planned snack times only. I would offer him the same food as everyone else, perhaps offer a good variety on a plate to see what might tempt him. My kids love 'picnic' meals - chees, meat, bread, crackers, fruit, etc all on same plate. Allow yoghurt but only one small size one at lunch or dinner. Not several or at every meal. If he screams, refuses or throws food, calmly tell him 'it looks like you've finished' and get him down. If he chooses to come back before meal has ended for everyone else, let him but present the same options again. If the meal is over, it's over and he needs to wait for next designated meal or snack time.
I also didn't restrict 'pudding' - so no 'if you don't eat x you can't have y'. I decided in advance what was for the main meal and what was for after. Kids had what they wanted of main, then had pudding after. But not an alternative or extra pudding to make up for lack of main if that makes sense?
I would anticipate a lot of resistance initially but kids crave rules and boundaries, and I think if he sees you are really serious then he is likely to comply pretty quickly.
Good luck!