In the simulation, there is no inductance or resistance in any of the wires. Capacitors and wires are superconducting. If you want to make the simulation behave like a real world circuit, then put in some trace resistance and inductance, something like 10mΩ and 10nH, that should smooth out the spikes some. Another thing is to put a cap to ground on the nets being switched in the pF to nF range.
Check the power on the mosfets, they shouldn't be very spiky. Another problem that you may be having is turning on two mosfets at the same time. Make sure you don't have crossover on the gate voltage and allow some time so both FETS are not turned on.