As a social services/family services professional, you have a strong sense of where you want to live and I applaud you for that. I have sold many homes in the Raymond area and my customers were mostly choosing houses not towns based on what their family needs were and what their money would buy. Usually money goes a little farther in Raymond, so you can buy a larger/nicer/newer home there for the same money as an smaller/plainer/older home would cost in one of the more seacoast towns.
But that doesn't solve your problem. Right now you are also faced with "summer rentals" which will begin on or about Memorial Day and are always expensive. You might find a home in the Durham area when the University lets out and the students leave for the summer. That will occur in only another month. If you could stay where you are or find a roommate for the summer, you will be able to find a beach area winter rental--which will be quite inexpensive, but will only be a 8-9 month solution.
One thing I said in my earliest post is that generally rentals don't find their way into the MLS. (Some do, but most don't.) This is a function of landlords not wanting to pay a Realtor's commission. But rentals are available if you know where to look. I would try Craig's List, also University housing at UNH or other colleges, often they have a list of local landlords which they hand out free as a service to the students. (You might find exactly what you want at White Pines College in Chester) Or you could both read and put flyers up on community bulletin boards--I always had good luck with bulletin boards in laundamats.
Anyway, wish I could help some more.