How to replace a relay with a MOSFET?
Try this: -



You need to find a P channel MOSFET with suitably low on-resistance that can be activated acceptably with logic level voltages. For instance the NDT25P03L is logic level driven and has an on-resistance of below 0.1 ohms.



R3 in the top schematic can be about 10 kohm if you are not too bothered about switching speeds.