Travaling and rental hunting with a dog

Does anyone have any suggestions for me! I will be relocating to Ajijic as soon as my house hear sells. I plan to drive and have a 50lbs dog. I want to stop off in Monterrey to visit family then continue to the Lakeside area.
When I get to Lakeside, I will need a place to stay while I look for a rental. Do any hotels accept pets?  I also plan to tow a very small trailer with my personal belonging (my Jeep can't be used to safely store them) and will need a place to store it.
Can't wait to start my retirement in Mexico!!!!

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