Is some left wing group going to sue to stop that?

No, but it's not something the President is going to host. It's a private party that the President is invited to, not an event that the government is sponsoring. I can't imagine that any of the folks involved want to deal with the logistics that go with moving the event into the actual WH.

Only if the building was ugly.

Nope. If this was Obama, the right would be suing and screaming and talking about how he was violating the Constitution all day long.

Again, it's literally one of the most common things in politics - supporting stuff your "team" does when you would bitterly criticize it if the other "team" did it, and vice versa.

So you need to step back and look at the substance, rather than looking at whether one side is being hypocritical or not (hint: they both are, all the time, in these cases). Here, there doesn't seem to be any justification for the President having the authority to do this. It's not one of his inherent Constitutional powers, and there's no statute authorizing him to build buildings on federal property just because he decides to. That's Congress' call, not his.