Are you flying to Saigon from USA on the UA flight? If so, you might consider flying Saigon-Bangkok and back on TG--as they are both Star Alliance, it should be no problem on the return journey to check your stuff in BKK all the way back to USA. You'd just have to show both BKK-SGN and SGN-USA tickets and get them to manually put it into the system. Not sure if they can give you boarding pass in BKK for SGN-USA flight, but you could deal with that if you had to in SGN. Flying Vietnam Airlines to SGN-BKK and back might present more of a problem, as they don't yet connect into the interlining system too well (if any) and you'd probably have to find a way to reclaim your bags and then recheck. However, they might be able to either give you escort or provide a transit visa to get you back around to transit side.