My kids are only 5 and 8 and have already, in the last two years, said, on a number of occasions, completely unprompted, and totally at random, things like:
"I don't want to go to mommy's house"
"I want to stay here"
"I like it at your house better"
My response?
"Your mommy loves you, and starting tonight, it is her week to show you how much she loves you, and spend time with you. I love you very much and love it when you are here, but your mommy needs your love just as much as I do. "
Then, they go, the world hums along, and I get to sleep with a clean conscience knowing that I succeeded in my job as a parent, by making sure that my kids respected the roles of both parents in this situation. That stuff comes up every once in a while, and I gently redirect them away. Sometimes, I ask them why they would say such things, and I listen to their answers, tell them that they need to talk with their mom about the things that bother them, and then inform my ex via email what was said, and remind her that I supported her role and didn't indulge any of what they said.
If my kids ever listed anything of grave concern, that would be a different matter, but so much of it is minor preferential stuff. They have more fun at my house, they like the food better, there are more clean clothes, they get to see more of me because my ex works some nights, (which means that on those nights that they are at her house, the boyfriend watches them, which was tough at first, but I got over it).
So much of what drives their preferences and desires at this age can be found in Maslow's Hiearchy of needs. Whichever place best addresses those base needs of shelter, food, routine, etc. is inevitably going to appeal to them more.
I know that my household has more of that, as my ex is a flake with money and is incredibly disorganized. That being said, she loves our kids just as much as me, and does the best that she can. Some day, my kids might get to their teen years and express a very strong preference for either of our residences, and we will both have to deal with that reality, but until that day, they are simply adorable little humans that are driven by very basic needs, desires, and wants, and attempting to cater to their weekly shifts in those factors does nobody any favours.
Unless there was a real concern about my children's well being, I would never encourage any of their efforts to pick one house more over another. That undermines me just as much as it does my ex, because it teaches the kids that parents are disposable and switchable.