Just to give a quick "opinion" answer.
Costa Rica is one of the best opportunities you have to catch "big fish" (Sailfish, Mahi, Marlin) without having to go very far out.
For example, on the East Coast of the US, depending on where you are, you have to go out 35-60+ miles to catch big game fish, . It takes HOURS just to get out there, the water is usually rough, and then HOURS getting back. This would DEFINITELY be "boring" and hard to do with young children, and the chance of seasickness is high.
However, in Costa Rica, it only takes about an hour from dock to fishing grounds, even less depending on which "big fish" species you are going for. Also, the mainland of the country runs from the northwest to the southeast and provides a “cover” from high winds and makes for extremely calm waters compared to offshore in the US.
Furthermore, big game fishing in Costa Rica is less expensive than in the US for example, because you don't have to go as far out, and don't have to use as much gas.
SO, what I am getting at is, you should give it a try. This is the "easiest" chance your husband and kids have to go catch "big fish".
As far as allowing your kids to stop and swim- if you pay for the boat, you pay for the boat, and I am sure they will let you do whatever you want in that half day or full day time frame. You can do circles in the harbor if you want to! HOWEVER, you are paying a premium to go deep sea fishing (a LOT more than a snorkeling trip costs), and you only get a set number of hours. Using some of the time you paid to go fishing, to go snorkeling, would be overly expensive, and I doubt they would lower there price to take you snorkeling, because they would be losing money and time from what they could get from other fishing customers. Paying for a fishing charter, but using it to snorkel would have to be the most expensive snorkeling trip you could take!
My suggestion- take a HALF Day deep sea charter, and take a separate snorkeling trip! You will save yourself a good chunk of money snorkeling off a snorkeling boat!
Edited: 10:12 am, September 10, 2013