You must purchase Mexico insurance from a Mexico Insurance Company, it is there law. US insurance is not recognized in Mexico. You will want to make sure your policy includes bail bonds, very common in accidents in Mexico that you will be required to post a bond. Some US insurance companies will tell you they will cover you in Mexico, but typically restricted within 25 miles of the border and does not offer third party coverage (liability).
US policy will cover Canada.
Europe Auto insurance is a separate policy.
One of the main reasons you must purchase separate insurance is each country has different laws so it is difficult for one insurance company to write one policy to cover all countries, then staff each country with claims adjusters etc, then figure out how to rate the policy.
Most countries will offer a short term policy as well. Good luck!
2009 American Eagle 42'
Trailering HD Road Glide and Saab 9.3 or Cadillac Escalade ESV