It goes straight to voicemail, as if the phone was switched off. The person doesn't know they've been blocked, unless they get suspicious that your phone is never on and get someone else to call from another number. Then when the other person gets ringing literally seconds after the blocked ones call goes to voicemail, the blocked ones know they've been blocked.
Any texts go into a blocked messages folder and you don't get a notification you have a text. So you can go looking for blocked messages if you want, but if you don't do that you'll never know you have them.
OP use this hijacking of your holiday to disengage permanently from these people. Even if they're relatives. They're not friends, they're stressing you out, they're being extremely selfish and they're trampling all over your boundaries. That's 4 very good reasons to never speak to them again.
Don't bother with all the explanations and attempts to pacify them etc. If they won't accept a "no" after they've rudely invited themselves on your holiday, then just switch off your phones when you leave for the airport.
You don't need a phone on holiday anyway. You're together! Nobody else needs you. Even horrific things like someone dying while you're away - they'll be no less dead if you cut your holiday short and return home, so just enjoy your time in peace and whatever is going back home will still be there when you return. Relax and properly switch your minds off, knowing you're uncontactable for the next two weeks. That's part of what a holiday is about.
If you want to get online buy a cheap local phone and SIM.
If you choose to just block them but leave phones switched on, be prepared to ignore any calls from unknown numbers or from anyone who isn't eg your children (and make it clear to DC not to contact you about these people no matter what). You don't want to have to be fielding calls on their behalf. Just knowing something has gone wrong with the guy's health will stress you out and spoil your holiday, even if you don't help at all. Try not to be on the same flight as them either.