Is this the only reason you want to transfer? I could understand it better if you currently commuted an hour, but 20 minutes isn't long.
Is the other store really that much better? A larger store in my area was so poorly run that the whole back room team left and they had to have TMs from other stores come in to get things put away so floor replenishment could happen. They "stole" our SD and she recruited a couple of TLs from my store to get them back on track. They're doing a lot better now, but it was a real mess for quite a long while.
Are there TMs you can talk to at the other store to get the real story about what it's like to work there?
After some investigation, not just "grass is greener" thinking, are you sure it's worth it to shave 10 minutes off your commute time?