So we have a mouse problem, and our landlords are pretty worthless when it comes to solving it. They're coming from underneath our kitchen units, which are all raised about six inches, with wooden skirting board in front of them. I've closed two small (2x2 inches, ish) gaps with thick cardboard and white threaded tape, but I'm unable to do the same with the dishwasher since the door needs to be able to open. Currently, we're shoving a towel in there whenever the dishwasher is closed, and removing it whenever we need to open it. It's inconvenient. Is there a better solution? Something that would fill the hole, but stretch, expand, or unfold when the dishwasher is opened?
It's not the interior holes you need to deal with...it's the external ones. They're getting in the house somewhere/somehow and that's what you need to block.
The simplest way to do that is find the holes, and stuff them with stainless steel wool. The rodents will not want to chew through that.
Plugging the interior holes/gaps won't do much. They'll just eventually chew a new hole elsewhere.
They'll probably find another hole, even if you do cover that one up. Get a cat, or other pest exterminator; or reduce the food available for them. Or move.
As a quick fix you could try one of those expanding foam things. Just get it in a spray can at the hardware store and spray into the gap. It will then expand to fill the hole. Once it is dry you can clean it up a bit to be more presentable with a hacksaw blade. This method will only work for small-sh gaps though.