Well if its gotta be done its gotta be done - is it a good 38 mile e.g motorway/duel carriageway? I only do a 3 mile trip to school and the novelty wore off v. quickly but I have no choice as its the school we've been allocated rather than chosen. I think seeing as its a definite move YANBU (but you know that really don't you? )
If it's only for six weeks and you think you can handle the driving, then do it. My ss, sd had to travel 25 miles each way (50 mile round journey) to and from school when we lived in Scotland, they just read/did homework/listened to their ipods. (This was one of the reasons why we decided to move back to England, as they were only at the beginning of their secondary schooling and it became depressing doing the drive everyday!) I would ask yourself if you can afford to travel that amount everyday, it gets very costly for petrol, car wear and tear etc, although with us because there was no bus service we were paid a set rate per mile by council that helped towards the costs, but if it's for a limited time then would seem do-able.
I was at the other end of school - A-level year - when my family moved 40 miles away from school. Mum and I drove 40 miles each way, mostly M6, from October half-term to the end of the school year. Of course, this was in the dark ages when petrol was cheaper than gold - although it did mean my parents having to part with a much loved vintage car that did 12.5 miles to the gallon!
Definitely worth it, IMO, for a short period of time.
Getting into the right school will be priceless in terms of your daughters education. a few weeks of driving will be fine if you are happy to do it. She wont suffer but will benefit from being in a good school