I had this exact thought. If you're going to be brazen on a public forum about how you hit your children, at least own it. We all know you're not "tapping" them, you're causing them physical pain or it wouldn't be a punishment, would it? Taps don't cause physical pain. If you're that confident you're right, then be honest about it. You're hurting your children and you're proud of it.
OP, sorry I haven't read every bit of the thread (because jeez) so I don't know if this has already been said, but my eldest had a hitting phase and I shut it down by staying completely, robotically calm (hardest thing in the world) and just removing myself, the other person, the toy etc. So "no, I don't play with people who hit me," "no, that's not safe for your brother so I'm moving him away now," "no, that's not how you use that toy so I'm taking it away now," etc. Take yourself or baby out of her vicinity and remove the attention.
Re. separating the kids, and someone asking what do you do if they just keep coming back - baby gates. "No, it's not ok to hit, we're going to play in the other room now." If you were playing a game, that's end of game. If playing with a toy, end of using that toy etc. So you can go back to the 2yo once she's calmed down (it's not a time out as such) but don't keep doing the thing you were doing before. "No, I don't want to play that any more, we can try again tomorrow," etc.
For us it worked because there was no massive reaction, but she spoilt it for herself because she ruined the game etc. She very quickly learnt not to! The good thing about the "I don't play with people who hit me" line is that it models it for them too, and I heard her say it to her cousin once. Made me really proud actually!