Sorry I can't give you any help with the root part since I've never done it but I could let you know what to look out for if you want this action to occur with another app.
Pretty much when you plug the phone into the car dock... an Intentis created. If an app like Custom Car Home or another other associates itself with that Intent then the user will receive a selection dialog asking them which app they would like to launch for that intent/action.
If at the moment the only thing that happens is the Samsung Desk Home is automatically launched, then this is probably because Custom Car Home has not associated itself with that particular Intent.
From the sounds of what Tasker can do (and I hear it can do a heck of a lot) this should be manageable through it. Try to set up an app launch on a specific condition. That condition is when the phone is docked into the car dock.
Tasker will then associate itself with that Intent and fire off your desired app.
Hope some of that was a little useful. Sorry I couldn't be much help.