So whilst I dont think its unreasonable for a 17yr old not to want to look after your dog, I can completely understand why you would be annoyed with the offer being retracted.
Maybe DS offered and hadn't really thought about the responsibility properly. The thing is, you wouldnt begrudge your DS for not wanting to be responsible for a younger teen sibling, so not really sure why a dog would be different when they level of commitment is (almost) comparable in terms of company, stimulation, exercise, food, etc.
Why is your DC not looking after the dog such a big issue that it stops you going on holiday? Is it really the inconvenience of them changing their mind and having to make other arrangements that you're not comfortable with or are you annoyed that your DC may not care about the dog as much as you?
Can book a dog walker for at least once a day, and a house dog sitter whilst he goes away? DS should probably fund this since they have changed their mind about it.
Unless your DS has form for thid on a regular basis, then I don't get what you're going to achieve by cancelling their tickets for an event in 2 weeks time (unless this is when you're going away) AND cancelling the ski holiday that you decided to fund later in the year.
I know some people find it astounding that you are still funding your DS holidays, but that seems to be something that you're happy to do and actually a lot of parents do this even for adult DC in later years in different ways (help with mortgage deposits, childcare, etc)