Can I sue my contractor for damages to my home during reconstruction and do you think I can find a lawyer pro-bono if it was serious enough?

From your explanation, it appears that the driver of the car is at fault and not the contractor. Why don't you sue the driver.

You can of course sue for the damages but I doubt you would get an attorney to handle the case on a contingence basis. You certainly would not get anyone to handle it free of charge which is what pro bono is.

Pro Bono means that the lawyer works for free. This is the real world! Only some small cases might be handled by a lawyer for free, but in your case, you need a lawyer to sue whomever ran their car into your house. Under Michigan law, the driver of the car would probably be responsible for everything that resulted from that stupid act. Of course, you can also sue the contractor for causing additional damage. However, you will have to hire a lawyer and be responsible for paying the lawyer. There is no such thing as a free lunch.

You don't get free medical care except at the ER if you are a charity case, you don't get free dental work. Why would you expect to get free legal work? Who will pay the lawyers staff, his rent and his general overhead while he works for you for free?

You will not get a pro bono attorney. If the damage caused is below $5,000 - $4,000 (depending on state), you can take them to small claims.