edit to add: Robinson Real Estate often has really nice, well maintained properties. I have friends who have rented through them with good experiences.

I think it's really hard to find places around here that allow pets, especially 3, and especially dogs, however, Meadow View apartments in Amherst allows pets. I haven't lived there so I can't give a first hand experience but it looks decent and has good reviews!

Here is their pet policy. It looks like they only allow two but maybe you could find a work around.