TBH, I would tend to prioritise my children within reason, but the details do matter.
You only get NHS orthodontics if you are level (I think) 4, which means a risk to health, like a massive overjet. And, even then, it can be incredibly slow and they don’t use the most modern materials.
Her teeth may not be that bad now, but they do tend to get worse with growth, of untreated. And, they do say the younger you start, the better the results.
I would find out how bad hers are and how bad yours are. If similar, I would prioritise her. If you are a lot worse, I can see a case for prioritising yourself. You can then explain to her clearly why you have made the decision.
Both mine currently have braces, at a cost of close to £12k, so it can be a tough decision.
Good luck with whatever you choose,