The tenant had clogged the old cast iron sewage pipes with baby wipes and other garbage (e.g. pens.

Many household products are labeled and marketed as DISPOSABLE and/or FLUSHABLE; many baby and adult personal hygiene products, along with household wipes and cleaning towelettes are labeled both disposable and flushable.

They become babies and they revert back to the TESTING PHASE.

Dude baby steps.

If your tenant, or their guests (which may include children) or their dog, is harmed by a wild animal with sharp pointy teeth living under the deck with its growing babies, that they informed you of and asked you to get rid of - then I see "liability" on a neon sign hanging above your head.Use your common sense here, instead of looking for some technical loophole.  

My second question is, "How can I provide better service to my tenant without babying them?"

In your profile photo you are holding a baby so I'm assuming location and school district will be super important.  

The cats I had would just watch the mouse run across the room while they laid there looking bored.There is never just one mouse and it really sucks to one morning open up a drawer to find a nest of baby mice. 

However my new tenants just had a baby 2 weeks prior, and I went to inspect the house, as agreed, and they happened to be home and watch me like a hawk. 

I had a somewhat similar (though not quite on point) situation last year...tenants were husband, wife, and newborn baby.