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Your instincts would seem to be better than your husband's. Having someone else do the driving and avoiding situations which could compromise the amount of money he could be awarded would be in his best interest.
I couldn't possibly tell you if he's manipulating anything without being privy to his medical reports, his restrictions, and any other relevant legal documents. I'm only suggesting that if he's made a worker's comp claim and he's supposed to follow doctor's orders and refrain from certain activities, he doesn't do himself any favor by disregarding that.
As for whether you have any kind of a case, you can certainly bring this evidence up in Family Court if you feel that he's ducking work and/or fraudulently padding his injuries to duck or keep down his child support obligations.