I’m sorry. But I think it’s completely unacceptable and selfish behaviour on his part.
As you say, if this was an emergency, understood. If something came up, also understandable. But if he has committed to plans with you, 6 months ago, then as his partner, you also deserve some level of prioritisation.
If he wasn’t able to do this, he shouldn’t have committed. And if he didn’t want to, then he should simply be honest with you. In your shoes, I’d be having an open, non confrontational conversation with him about where he is with things. I would ask him if his view is going to be that all of his time with his daughter is a number one priority. Because from what you’ve explained, you’re getting no weekends away/ Saturday nights out. Ever.
Now if he says, yes my weekends with my daughter are my priority. Always. And they will be for the forseeable future, then you have to go away and think about what you want out of a relationship and if this is it.
I think it’s that simple. There a plenty of people who accept this. And they see their partner when their partner is available and remain relatively independent When the partner isn’t and have an active social life away from the partner.
Or they come to the realisation that actually, from time to time, they want to be prioritised. And whilst their partner is admirable in prioritising their child, they themselves want someone who can prioritise them once in a while.
It all comes down to what you want. Oh and I would still go on the night out. Who cares if everyone else is in a couple? I’m sure the other couples won’t care and will make sure you feel included. Don’t cancel your plans.