Last summer I was looking for a boat to fill the same family/fishing parameters you listed. I bought a Northwest Jet, 19' Competitor with a 351 redline and Amer. turbine pump, and have very pleased with it. It seems to serve both functions very well. However, the dollars on even a used one may be a little above what you listed.
The advice on power in the above post is a good one and very important. The extra power will probably be more important on the family outings han the fishing if you are going to pull tubes or kneeboards.
Good luck, and I think you will find the money well spent on a boat.