Criminal action for "accidental" property damage

There are three potential crimes: vandalism, trespass, and fraud. A conviction on any of these counts would require the state to prove bad intent, for example you would have to prove malicious intent for vandalism, or that they knew that they had no permission to be on the roof. Their defense could be as simple as "I'm so sorry, we got the wrong address". On the other hand, if they "got the wrong address" on a regular basis, it is at least reasonable to think that they are running a scam. Still, for a criminal conviction, you need more than a probability that they had an evil intent: you need to rule out negligent or reckless conduct.

Even though it was a "mistake" they did ruin the roof "on purpose" - their intention WAS to destroy (strip) the roof.

No. Their intention was to repair the roof and improve the property. That damage was done was entirely accidental. Most jurisdictions require malicious intent, but even those who don't require the damage to be intentional.

After this error, the company apologized but rather than offer to re-shingle for free due to the error, they offered the family a "reduced rate".

This makes me wonder if it really was a mistake or whether it was a scam to get the family to employ their services at a "reduced rate" at which they could still make a profit. If there is evidence to support this, then their intent was malicious and various vandalism and trespass laws would likely apply.