Me [35 M] with my friend [35 M]. Friend pinched my 3.5 year old daughter's nose for disciplinary reasons (or maybe as a reflex?); I proceeded to kick his family out of my home

We were having a nice BBQ at my house on fathers day, with my friend, his wife and their 2 young kids (3 and 2). We've known these folks for years, they are our best friends, and we have kids that are about the same age as theirs so we've grown even closer in the last few years.
At one point during the BBQ, my 3.5 year old daughter started banging on the water heater enclosure making a loud noise. I'm manning the grill, and my wife was talking to her friend, so my friend, went to see what was going on and proceeded to pick up my daughter. To this, my kid got upset and smacked my friend in the face. He responded to her attack by pinching her so hard on the nose that she started crying hysterically. As he brought her closer to me, I saw that she had a very noticeable red mark on her nose. I asked him to hand her to me, and told him, "that was way too hard, bro". I took my daughter inside to console her and sat on the couch trying to make her feel better. My wife came and sat next to me and I told her that I would like to be the one to make my daughter feel better as my daughter was very attached to me at the moment, so my wife rejoined the group.
After a couple of minutes with my kid, and me trying to make sense of what had happened, I grew very angry and resentful. I went outside and forcefully told the couple, "you need to go, now." No cursing, no yelling, just authoritatively giving a command. My friend made a pretty weak apology, and his wife said, "he's sorry he pinched you, but you shouldn't hit." To which I responded, "doesn't matter, she's only 3 years old." The couple then packed up their kids and their belongings and left my house.
Here are the issues I am contending with now

1. My wife is upset that I made a unilateral decision to kick them out. She agrees that what my friend did was wrong, but didn't like how I ended the BBQ. I think she's very concerned about the friendship, where I, quite honestly, am OK with ending it unless some serious amends occur.
   
2. Can the friendship be salvaged? I'm thinking my friend would need to apologize to me and my daughter, and we would have to set ground rules on correcting the behavior of our respective kids. Personally, I would never physically discipline any child that isn't mine, and I would be very cautious to even scold a child unless it was something very serious or dangerous.
   
3. Did I make the right decision kicking them out basically immediately after what transpired?
   

It was a very sucky thing to happen, especially on fathers day. I too would be sad if the friendship was over, but I'm the protector of my family. In my mind, something like this should never ever have happened.
TL;DR: Friend pinched daughter's nose for disciplinary reasons, or maybe as a reflex. I kicked him and family out of my house.


Source.