When we turn on the water anywhere in our house there are bursts of air, it spits and sputters sometimes for several minutes. It also does it in my sister's house next door as her house is on the same well as ours.

Sounds like either the check valve is stuck open at the well pump and not holding the water in the pipe from the pump to the house or you have a hole in the pipe in the well and allowing the water to drain back to the well. The air in the pipe to the house is then pushed into your holding tank when the pump comes on. Good luck, Mike