When my son was about 3 or 4, and like your kids, was taking lessons and doing well, I started shopping for a piano. I bought a Steinway Model "C" (7'4") that needed work, had the work done, and got a beautiful instrument. It made all the difference in my son's growth as a pianist, compared to other kids at his music school, he always had a better and more varied tone. It worked out in the long run, he's now 17 and is applying to conservatories here in the Northeast (US).
On the sound and neighbors issue, I would look into some acoustical isolation materials. Do a Google for "mass loaded vinyl" and read up about the subject. Note that this is not the kind of material that they'll sell you at a carpet shop. This is technical, industrial stuff. It's heavy and expensive. But it is effective. I did have a complaint, years ago, and I hung sheet of mass loaded vinyl on the walls near the piano (hidden by decorative quilts), put a sheet under the carpet, and also used these materials to de-couple the legs from the floor - a big source of sound transmission. The neighbor actually thanked me and told me the piano problem was resolved.
Last, I don't think the size of the piano will make that much difference in terms of disturbing neighbors. But if you're considerate with your hours of playing, and take some steps to reduce the transmission, and if you're neighbors are reasonable people, then you should be ok.