Legal is one thing. Company policy is another. Tax wise as long as you keep all expenses separate you should have no issues. Military as well as federal employees do it all the time. They go overseas at government expense, do their job, go to another hotel if they are smart, spend their vacation time, then fly back at uncle's expense.
Well first, I think you have to buy a ticket to Europe and then to wherever your vacation's gonna be from there. But your ticket to go home shouldn't be a ticket from Europe to Home. It should be from the Bahamas (or wherever the vacation spot is) to Home. I'm not too sure, I'm only a teenager.