Hi Janis,
I lived in Majadahonda for 5 years, although I think other posters have lived there more recently than I. Anyway, I can tell you that there is no metro, but the buses are very convenient. As for being reasonable, do you mean price-wise, or other-wise? I like Majadahonda a lot - it's much more open than the city, with lots of parks and green areas, but it's still very close to everything. Almost everyone lives in apartments/condos, and I'm sure you can find something to rent.
If you plan to rely on public transportation, be sure you're either close to the rink or there's a bus that you can take there. Majadahonda covers quite a large area!
Service dogs are allowed on public transportation - I don't know about other dogs - I doubt it. But Spain does recognize service dogs. I had a friend there who trained one.
I'm not aware of an artsier part of Majadahonda, but Madrid's so close!
Good luck with your move!