Due to this, the tenant with the dog wants to break the lease because they do not want to get rid of the dog.

Never heard of them before....but your typical real estate "mentoring" guru will invite you to a free 2-3 hour session, and convince you to come to all day on Saturday or 3 day weekend course for $299-$399, when you are at that course, they'll convince you to be a Big Dog player for full on mentoring at $15,000-$50,000.   

If one of your tenants gets bit by a dog, falls off a ladder, etc. and they have a bunch of medical bills they can't afford, they almost have no choice but to sue whoever they can to get the money. 

Humans cats and dogs, goldfish, tweety birds, not horses or other farm animals of any type.

The big difference from my situation when I was not held responsible is that you notified them that it was a hazard, and have an arborist's professional opinion that it was an urgent situation needing to be take care of, and photo evidence.

I am getting started with Bird Dogging right now!

I have had it for 5 years, and I have loved the thing, but I have a big dog now that needs cargo space.

I am looking into My lead dog!

Could you walk dogs and or babysit/housesit for your neighbors? 

I'm not a big fan of mixing family and business because it can destroy relationships.My favorite recommendation is the one nobody wants to hear: work like a dog, save up, and buy things you can afford to pay for.