I'm pretty sure that discharging a firearm in a residential area is a no-no, however there are communities that allow landowners to dispatch unleashed dogs on their properties, usually where there are livestock, such as poultry or other animals at risk from maurading dogs. I would check with your local police about the threat.

The screw in the tire is suspicious and should be reported to the police as a vandalism complaint, so that there is a record of the incident. Most "bullies" are cowards and windbags, hence the verbal attacks and threats of lawsuits. It would be interesting to find out if he's ever filed one. Some jurisdictions have online databases of civil suits searchable by name. Might be interesting to find out.

The key thing to keep in mind is that your MIL has to live there and if your presence is temporary, then perhaps it might not be a good idea to heat up the situation.