My twins are 7 weeks old. They were both head down and after 19 hours of labor, 4 1/2 of them pushing, we ended up having a C-section to my dismay. Five days after the delivery, I ended up having a pulmonary embolism or blood clot in the lungs. I learned later in a converstion with my OB that there is a greater risk for a PE in a twins birth and a C-section birth. It is still quite rare though, so do not panic.
I would encourage you to try for a vaginal delivery. My second baby became head down the weekend before we delivered which was at 38 and 1/2 weeks. I also read and was told by our doula that once the first baby is delivered it is not uncommon that the other will change position and become head down on their own. Also, there is a maneuver called the Leopold move that OBs can do after one baby is born. There is ample room in the uterus after the delivery of one baby so they can help assist the other baby to move into a head down position.
For my labor, having pushed for so long, I had two places or recovery as you were describing above. I didn't have vaginal tearing but had the swelling and such. I can tell you it was not difficult at all to recover in both places. Once the babies arrived, nothing else mattered!
Good luck with your delivery. May you enjoy a wonderful experience with your two new blessings.