Her sister lives around the corner and is free to collect her much earlier than I am so I did wonder why she was insistent on me being next of kin and her transport and why she wanted to stay at mine for the weekend
Because, @tripleback, this is not about pragmatism, it is about your g/f wanting to feel looked after by - you know - her b/f.
You seem a little blase about the effects of general anesthetic.
The fact that she'll only be out for 10 minutes is immaterial - she will be woozy, disorientated, & prone to low mood for a few days.
Having a wisdom tooth out fucking hurts, in case you were also in ignorance of that. People tend to want to feel comforted afterwards. Maybe your g/f's sister IS the better option after all - because despite your claim to "love" your g/f, not once have you commented on how nasty the procedure she is going through will be for her, nor made any remarks about how she might be feeling.
Here is your chance to actively demonstrate to your g/f that YES, her feelings matter & YES, she is more important to you than a drink with your ex.
If you cannot do that willingly, wholeheartedly, & emotionally generously, I suggest you do your g/f a big favour, ditch her, & go & get pissed with your ex instead.