Can a high voltage difference force a MOSFET open?
could too high of a voltage force the MOSFET open?


If by "open" you mean "conducts current", yes. If the source-drain voltage is in excess of a maximum specified in the datasheet, the MOSFET will experience avalanche breakdown. If the current through the MOSFET is not somehow limited, this will result in failure of the device by overheating.

For an example, I've picked the very common 2N7000:



This particular MOSFET is not rated for avalanche operation, so you do so at your own peril. However, some power MOSFETs, especially those intended for motor drive applications, will specify a maximum energy the device can tolerate in avalanche breakdown conditions.

This is especially relevant in your situation, since you say that you are switching solenoids, which are very inductive. When you turn the MOSFET on, current builds in the solenoid until it is limited by resistance, and a strong magnetic field exists. When the MOSFET is switched off, the current must continue flowing somewhere, and the energy stored in the magnetic field must go somewhere else. Since you have not provided any other possible path for the current, when you switch one of your MOSFETs off, the inductive kick of the solenoid will drive the MOSFETs into avalanche breakdown, and quite likely damaging the MOSFETs, or any other components connected to the power supply.

The usual solution in this situation is a "flyback diode". I know this has been covered many times on this site, and someone will suggest a better reference, but in addition to searching for "flyback diode" generally, check out Questions About Inductors.