Here's your problem: you gotta stand up for yourself. I often find it helpful to ask myself, "What would Cave Johnson do?". He sure as hell wouldn't put up with his uncle's baby giving him bullstuff.
If your uncle says "you're just grumpy", you shoot back: "You'd be grumpy too if your uncle kept shoving his baby on you while you were trying to do something productive." If he says "You just have issues", you say, "I have one issue and it's the fact that you can't take care of your own damn baby." (damn is optional). If he says he'll laugh when you have kids someday, you say, "Go ahead and laugh if it happens but in the meantime take care of your damn baby so I can do my work in peace." (again, damn is optional).
Other possible retorts: If he says you were a baby too once, say "Yeah and I was one irritating little bitch (substitute brat if need be) but at least my parents had the good sense to take care of me and not throw me at random relatives while they went out having fun."
The trick is to have a ready retort, and to show that your patience is running out for perfectly logical reasons. You're trying to go out there in the world (wide web) and do important things, but it's awful hard when his goddamn baby is slobbering over all of your stuff.
The above really only applies if you're 100% certain he won't listen if you ask nicely. Which, from what you've said, he won't.
