Since you’ve expressed some affection for Addictive Voice Recognition Technique (AVRT) it may be useful to point out that the AV loves future predicaments that in the past would be a Pavlov dog bell to trek on over to the liquor store. And you’ve clearly expressed “your” desire to drink for the joy of it, not just because of the predicament you have. That sort of honesty is refreshing here.
I found that once I was able to catch the AV and dissociate from that quest for pleasure ALL the time, EVERY time, I was able to solve problems better, faster, and more successfully, than when my unrecognized AV got me to stew in my own juices for lack of that habituated, wonderful assault of chemically enhanced stupidity.
In your situation, I would simply find the closest good kennel to my sister’s place for my pet, and while visiting go get it several times a day, and take it walking - even over to the sidewalk in front of my sister’s house. I would do it with expression of calm and even joy; and I would enjoy exploring around her neighborhood more than I would otherwise.
If I were to run into any neighbors and start visiting with them, I’m not sure what I would tell them about the pet situation, but it would certainly give me some options and put me in control.