Would a digital compass work reliably when installed in a car?
Gyroscope:  I'd have thought that it was worth working on the gyroscope data to see if you can us its known location in the car + car known geometrical performance when turning + what the accelerometers say to interpret the gyro result more appropriately. A "perfect" gyro should give you better results than "perfect" accelerometers. Reality and Murphy will make this less so, but it's still a shame to abandon the gyros. 

Magnetometers - aka compass: You'll have problems if you install a compass where it is affected by large items of ferromagnetic material.
Under a car dashboard certainly qualifies as a really bad location.

You can carry out a very low cost test by  taking any compass and holding it in various positions under the dashboard (still in sight) and seeing how it changes, Then turn the car 90 degrees and repeat.

Where it matters "real people" perform "compass swinging" to either produce a deviation chart or to make adjustments by the use of either small magnets or pieces of ferromagnetic (usually) metal. (eg Brass is very slightly diamagnetic (~= "anti ferromagnetic") and will also affect the field but much less and oppositely in sense. 

If you make a deviation table then it could be adjusted for in software.

Useful compass deviation page.   

They say:

In most cases, these difficulties can be overcome by 'adjusting' the compass. This is the process of placing small magnets around the compass site or of altering the positions of adjustment magnets within the compass body. Traditionally, it has always been considered a task for specialist compass adjusters and beyond the means of the average boat owner. 

This is no longer true. With C-Swing, preparing a deviation chart is now simply a question of selecting a suitable shoreside object, entering its true bearing from the chart, then entering its compass bearing as the boat is sailed on a range of headings. With the built-in maths package, headings do not need to be exactly on compass points and, if suitably spaced, as few as 5 are sufficient to prepare a full chart showing deviations at 10� intervals. Furthermore, C-Swing also computes a set of magnetic coefficients and gives guidance on placing corrector magnets and making adjustments.

That sounds hard, and it's not utterly trivial, but a bit of thought about what you are trying to correct for and how external magnets help will show that it's a fairly straight forward process. And, it's likely that intelligence-informed trial and error will allow you to do an OK job.
Here are people who do it do it for a living



According to the above page, here are people who didn't do it properly - USS Port Royal grounding in 2009. However, according to Wikipdia report it was not a compass error but a more high tech navigation system error followed by lots of human error that lead to the grounding. I'll leave the picture as it does make the point of what can happen if your navigation system is faulty. Just stay away from coral reefs with your car! :-). (Reef cost them $15M to repair. Ship between $25M &amp; $40M)



Useful page here

Wikipedia - historical - interesting

They say:


Diagram of a 19th century binnacle housing a compass. It has two soft iron spheres (Q) to correct for induced magnetization.