What is the correct etiquette when one would like to include the alternative proofs supplied by the reviewer
I would think that if the referee shared an alternative proof in their comments to the author, their very reason for doing so was so that you could include it in the paper.  What else would be the point?

I don't think you need to ask for permission.  It would be sort of like asking for permission to take a mint from that little bowl by the door of a restaurant - that's what it's there for.  You can ask if you really feel it's important, but it creates a slight amount of extra work for the referee and the editor who has to relay your communications.

If the alternative proof is such a major contribution that you think the referee ought to become a co-author, then of course that is a separate discussion.