In my skimming through Day By Day I found this reference for September 
11, 1876:

"The Clemens family returned home to Hartford [Sept 14 to Fairbanks]. 
The train trip from Elmira to Hartford took ten hours, and always 
exhausted Livy. On this trip Sam first hired a sleeping car, which gave 
the family privacy and lessened the stress for Livy. Their German 
nursemaid, Rosina Hay, was able to keep the girls occupied and Sam 
wasn’t bothered by other passengers’ talk and autograph requests. Sam 
promised that the luxury of a private car would be a permanent one for 
the family [Willis 103]."

Now, looking for references in Day By Day is difficult - I can find no 
entry of Willis but suspect it is Resa Willis.  I know nothing of her 
book but the Amazon write up leaves me in doubt.

"In Resa Willis's affecting and fascinating biography, we meet a 
dignified, optimistic women who married young, raised three sons and a 
daughter,..."

So, if anyone has a copy of her book, "Mark and Livy: The Love Story of 
Mark Twain and the Woman Who Almost Tamed Him",please see if any useful 
information might be had on page 103.  There is nothing about a sleeping 
cat in the letter to Fairbanks.

Thanks