Is it ethical to ask the postdoc employer to cover my trips for visa purposes as well as my main travel fees?
In the cases the I have known in the U.S., the relocation allowance is a fixed amount of money, and the university is fine with it being spent on anything reasonably related to relocation.  If this is the case with your university as well, then they'll probably be fine with it being spent on your combination of expenses---but if they combination of flights is expensive, you are likely to hit the cap and have some of the costs become your own responsibility.

The exact rules and regulations, however, can vary highly from place to place, so you really need to ask your university.