I would start off with a standard generously specced MOSFET type arrangement for triggering.
Look in Manual 3 about how to trigger a solenoid or relay. Easy stuff.
You will probably need extra surge-absorbing and decoupling capacitors.
For exact currents you will need a current sensing chip . There are millions around, take your pick.
You can then feedback the value in code to adjust PWM in order to get the correct current. You can use a simple PID type calc.
Quite honestly you can probably calibrate a current/PWM value that is good enough and maybe trim it with a simple cut-down PID if needed. It just dpends how fussy all this is. Do you know?
Whether or not you can drive a MOSFET directly I don't know.
You can drive it, but when you start upping the frequency it can go pants.
I'm bored with rattling on about Gate capacitance/charge so I'll leave that to others.
Without knowing all the performance characterisitics of the bits 'n' pieces I couldn't tell you whether a really fast or medium Fq PWM is best.
Do you know?
For safety/reliability etc I would use a MOSFET driver.
And I would say that , unless we have someone here who has doen EXACTLY what you want, then experimentation is needed.
What is your electronics skill level?
Your code skill level?
Your budget?
Your time frame?
Is this on a road going vehicle that will be driven anywhere near me?
If this is vehicular do you know about safe power supply design?
I'll leave others to do the deserved Nanny bit.
If you have little experience (and it sounds like it) then keep it in
your garden
Note: Numerous Data Sheets on MOSFETs and drivers can be viewed to see example schematics (circuit diagrams).
have a search on the Farnell site.