Please repost this in the Piano Forum, and I'm sure you'll get more replies. But to answer a few questions:
First, I'm not a piano tech. I've just been an avid participant of the Piano Forum for 1 1/2 years. So based on what I've read, I'd say there is nothing particularly special about your piano. I believe the mirror was a popular thing to do at one time (40s? 50s? 60s?) but are now considered a detriment, not an asset. A piano dealer will not give you much for this piano in trade. It would be better for a tech or more knowledgeable person here to to give you an idea of how much you could sell it for, but that would be my advice: Sell it yourself, then use the money to apply toward the new piano. My guess is you'll be lucky to get a few hundred dollars to maybe a grand, depending on its condition.
As for "small" pianos, all uprights are the same width, about 5 feet. The difference is how tall they go, and most people have the wall space once they've found the 5 feet in width. By all means, consider buying the tallest upright you can afford. You get a much better sound with a taller upright than the smaller spinnets and studios.
You don't say how much money you have, and that will really dictate what brands to which to steer you. I don't personally care for Yamahas, though you will be able to sell it if the children drop piano or move out. A good upright that gets a lot of rave reviews around here is the Charles Walter. I think they can be had in the $5k range. Other brands to consider are Pramberger, Petrof, Kawai and Schulze-Pollmann.
You don't say how old your children are and what kind of music they play. This also may influence which piano you buy. If they've been playing 8 or 9 years, they might be pretty picky about the action.
The usual advice around here is buy a copy of "The Piano Book" by Larry Fine (or borrow it from your local library). Study up. It has a lot of great advice. Then play lots of pianos (even if all you do is scales or chords -- or have the children play, though depending on their age and maturity, you may not want to base the entire decision on their opinion) in your price range and some beyond it to get an idea of a sound and touch you like.
Hope that helps!