So we can do this after you come back from your holidays? I will happily wait until then.
/ I will be happy to wait until then.
I know that the last one is common but is the first one incorrect?
In other contexts the <modal>+<adverb> is common though. I think I'd say 'Many town-dwellers would happily sell-up and move to the country', for example. In that case, 'would be happy to' would be right too; but I imagine it's less common... (Maybe this just my random preference.)