For me, "second home or vacation home" doesn't quite make sense if it's meant to be the big family investment. What is then considered the investment? "Second residence" doesn't really sound like much rental to me but rather more like personal use. "Investment" in that context would mean to me rather hoping that the value increases and to benefit a bit from it as a holiday destination. Or did I simply misunderstand that?
So if it is financially feasible, I would probably do something like that as my own little project with my money and my financing. If it is supposed to be more of a family project, I would say it is quite important that everyone is on the same page about what should happen with it and how you want to use and manage it. I believe there are indeed different options for organizational forms, but that exceeds my knowledge.