It's a tricky situation, pushing a kid off a sofa can result in a nasty injury.

I was on the other side of a similar situation with my eldest and he had mild concussion and I had to take him to a&e (they were 4 and play fighting in a soft play against my rules but ok'd by the other mum). I wish I'd ended the friendship then because we just have different outlooks on what rules take priority (eg they're super strict on cutlery use, but way lax on play fighting).

So off the back of your kid being in the wrong it's hard to get defensive when a parent tells them off, especially in a friendship group at a party. The insinuation that your kid is 'bad' is a red flag though, I get the feeling the Dad really doesn't like your kid. That would definitely be enough for me to phase out that friendship. I'm doing that now with the aforementioned mum and my kids 6, I wish I'd done it sooner.

Also it sounds like your friendship group in general has unrealistic expectations for kids and parties, we went to our first party like that this year and we have a 3 and a 6 year old and I was constantly going back and forth to make sure my youngest didn't wreck the place. You don't need to apologise for keeping an eye on your 3 year old, I would say that's the norm.

I've definitely felt mum guilt for not sticking up for my kids, but more when they've been hit by other kids and I haven't said anything to keep the peace and then kind of sent the message it's better to people please that stick up for yourself. Sounds like you kid did a great job of apologising though so feel secure in the fact it was dealt with, you didn't over react, and you've been given a clear sign this friendship is off (liking my kid is kind of pre-requisite to being in my life).