You will not be able to find a decent ride without spending what you call a small fortune. You might rent a car for a day and drop it off at Disney and re-rent for the return to Sanford. That involves all the paperwork in renting and than driving on roads that are strange to you. A good estimate of that venture would be $100.00 to $130.00.
The second option is to find a car service that will provide transportation for your family. There are extras included, but you go directly to the parks. Prices start at around $180.00 round trip.
They also have taxis and you pay around $100.00 one way and that is on a meter.
If you take the shuttles listed on the website, their prices are per person. Also they require you to pay a minimum rate of usually 4 passengers. Just the car service in a round about way.
Flying Allegiant you saved a bunch of money, rather than going into Orlando. The problem is that Orlando Sanford is about 45 miles from Disney compared to 20 miles from Orlando International.