I think he'll be glad to move away once he knows you are aware of his habit.

So, nope, you don't have to fix something immediately, even if it's a habitability problem.http://www.floridabar.org/tfb/TFBConsum.nsf/0a92a6...There are no laws that say you have to provide any kind of accommodations for an animal. 

If you give in to a threat, he may make a habit out of making further ridiculous requests/threats.

And then be required to get the place habitable within a certain time frame.And if the tenant discovers the place is not legal, they'll hold you over a barrel.My daughter's tenants didn't want to move, and I showed them they were wrong about it being uninhabitable.  

If the unit becomes inhabitable at any point, put her up in a hotel until it is habitable again.

Most tenants don't know that, and what they'll do, though, is start manufacturing habitability problems so they can break a lease.  

The mini blinds were newly installed by my husband, he might have done improperly wrong during the installation but the blinds still work and give privacy- Should I fix anything that is not affecting their daily use/habitability? 

If the repairs effect the safety or habitability of the unit there are further steps such as withholding rent that should be considered after a reasonable time to repair is given.

They will Not change their dog owning habits.

So do I stick with a known tenant who I now know their habits and have worked out most of the problems, or do I choose to not renew and start looking for new tenant?