kitcat, I assume from the schematic you are using one of the Allegro driver chips but I don't see pin 10 connected directly to the solenoid + supply. The reverse diode in series with this pin makes any connections to it useless.
I have used quite a few of the Allegro (formerly Sprague) drivers and I have never experenced any problems with them reseting any processors I have connected to them. One thing to keep in mind when using these multiple sinking or sourcing drivers is the current return path in the case of sinking drivers, and the supply path in the case of sourcing drivers should be as direct to the current supply as possible. Therefore in your application the pin 9 of your selected driver should have a seprate high current path to the current source "return" and the pin 10 should be going to the the closest point of the "loads" current source.
Dave Purola,