The reason home prices go up more rapidly in San Carlos and Belmont are because of the schools and also the location of both cities. San Carlos has one of the best communities and a nice downtown area for dining. Drive by on the weekend and you will see many families at the parks and ballgames with their children.
I don't think anyone on this panel is qualified to predict the future, but if we had to make an educated guess, every market or product has to do wth supply and demand. One huge advantage is the job sector is very strong here with Silicon Valley as the leader. Many companies on the Peninsula are hiring and will continue to hire. Remember, the job and housing market starts here and then spreads to other counties and states. Not vice versa.
If you are looking to own long term, say 7 years plus, I would say real estate is a pretty safe place to park your money. It's not always how much you pay, it's how long you plan on investing in it. No matter where or what the market is, I don't beleive in paying someone elses mortgage.
Now, if rates go up 1 %, buyers will lose approx 10% of their buying power, so there are a lot of variables that come into play. The best advice I can give is to focus on finding the "right" home and negotiating the best you can. After that, sit back and relax and enjoy your new home. You don't profit or lose money when the market moves up or down, only when you sell.
I don't know enough about the market in Mission San Jose to be able to offer you advice, but here is a suggestion. Why not hire two agents, one in MSJ and one in the Belmont/ SC area and whoever finds you the home earns your business. If you decide to do this, make sure to disclose this so both agents know where they stand from day one. I doubt any agent will know both markets, well.
There are also a few other areas that may work for you and your family if you would like to discuss it at a later time.