Lots of families like yours have wonderful vacations in Nicaragua that are really quite inexpensive if you plan them correctly
and as you have identified, keep some of the in-country transport costs down. Some folks want to plan every second in advance while another extreme has no plans other than to land and try to get to their first destination, which they may decide based on talking to someone on the plane, for example.
My usual suggestion is to take care of that first and last night in Nicaragua and then have some idea of what to do and where to go, but to keep an open mind and at a minimum, an attitude of “es todo una aventura” (it’s all an adventure) so that some spontaneous events might happen. I’ve seen families adopt this attitude and end up having lots of fun with it!
One option (especially if your flight arrives at night) is to stay somewhere near where the buses from Managua to SJdS pass by, so you can easily take advantage of the surprisingly not too bad public transport system here that will cost just a few bucks a person. Any shuttle service will charge at least $80 if not more for a MGA-SJdS.run, whereas a bus trip is around $3 p.p.
This approach to your first night in Nicaragua also works the same for other destinations to the south of Managua such as Masaya, Granada, Mombacho, Laguna de Apoyo, San Jorge (ferry to Ometepe), Rivas, Tola, Peñas Blancas, Cardenas, etc.
Regarding a volcano tour from SJdS, that would be do able as a day trip, but not ideal due to distance from said volcanoes. The closest would be on Ometepe Island; taking the ferry from San Jorge over to Moyagalpa, then probably taxi or tour to hike one of the two volcanoes. Best doing a volcano from Masaya, Granada, or Leon.
Finally, the cheap way to get to Granada from SJdS is to take a bus to Nandaime, then a different bus, Nandaime to Granada. Routes and timetables (take with a big grain of sal, especially on departure and arrival times) http://www.thebusschedule.com/ni/index.php
I hope that helps.
Cheers, Mike @ Farmstay El Porton Verde