It's not strange to me at all, Anna... I understand what you're saying, but we take our cat on vacation with us. I don't know where you're located, but many hotels and attractions here in the US are pet friendly and more are starting to be pet friendly all the time. We have a few things to make traveling easier but we've never had a problem and have been doing this for about 8 years now.
One thing we have is a large carrier for in the car (I'm talking about road trips here... if you mean flying then I've not flown with the cat, so I can't speak on that). The carrier gives her plenty of space and we've made cushions to put in it for the long rides. There's also a food dish that latches onto the side of the carrier.
When we reach destination and want to get around by foot, we have an enclosed pet stroller and the kitty loves moving around in it. When we stop pushing for whatever reason, she gets verbal that she wants to start moving again.
Bottom line is that we're all very close to our cat, too, and would never consider leaving her somewhere in someone's cage... so we look for pet friendly places (there are even restaurants in our favorite vacation spot that have outside seating for "pet families") and simply take her with us when we travel.
