So, I love the way you've thought this through.
And both scenarios are possible if you trust your neighbor to care for them while you're gone.
We travel a lot(like 3/4ths of the year) and chose sugar gliders as our companions. So they go where we go. We are currently travelling in a 5th wheel, and sitting in my stepson's driveway in the wilds of S Carolina right this moment. So I will always lean towards taking them with you...
When we travel without the RV, we take them too. In 6.5 years, we only left them alone 1 night and 2 days. It was the worst 36 hours of my life, but they were fine.
So back to your question. The experiences with traveling with gliders are priceless and if done well, can be a bonding
experience too. It will remind them that familiar smells (your scent) are a good thing. You become their safe place. And smelly things from home help too. Like their familiar bedding and pouches
that they have already marked.
First you need a travel cage. Something sturdy that can be seatbelted in. Then you need a cage for your destination. I use a $17 pop-up dog kennel from Walmart (be sure to take a wire bread tie to wrap the 2 zippers so it locks them in.) Then they need a wheel on a sturdy stand, or a treadmill so they have something to run their anxious energy on. A few foraging toys
to occupy them while they grow accustomed to their surroundings. Will there be a room where they can stay during the day away from other pets, or do you have a bonding
pouch so you can keep them with you? And can they stay close wherever you are sleeping?
Here's our setup:https://photos.app.goo.gl/HR7nm55qWr4RCTrx7
I've been using the same pop-up for 5 years and made modifications to it over time. If you notice, there is a PVC frame inside. We decided to go with that because of grandkids and "accidents"( the kind where they "accidentally" push it over, or "shmush" it.).
I have a piece of fleece for the bottom that comes out and is easily washes or shaken out. I use dishes for water(changed daily) and I keep the kennel off the floor and cover what ever it's on with a towel. ( You want to reassure your host and not ruin anything).
Does this all sound overwhelming, or appealing?
There are plusses and minuses to taking or leaving your glider behind. If you wanna hear more, or more specifics, please post and ask any questions you may have at this point...
. I'll be waiting!