Without doubt, gluing if done properly and carefully is best by miles. My father had a nasty four inch cut on top of his bald head. He caught it coming up too soon after ducking below a sheet metal sign!
The nurse at A&E glued it perfectly together brilliantly. There was barely any visible trace of it after a few months. Glue is painless to apply and completely seals the wound thus excluding infection the moment it dries. There is no need for anything to be removed it flakes away as new skin forms to replace it. perfect!
Stiches leave marks lines in themselves so drawing even more attention to the scar they leave. They are painful to apply. local anaesthetic is safer and better if it can be properly targeted and the child co-operates. GA should be a last resort. Sitiches can be burst, they often leave gaps to heal by secondary intention which creates a bigger scar as well as opening up underlying tissue to infection.
One poor girl, a teenager I saw on TV, had fallen through a dance floor which gave way. She caught her face on some sharp edge as she dropped though. This opened up a wound from her chin across her cheek to the top of her forehead at the opposite side. Glue might not have made her scar invisible but it would surely have been better than the hundreds of tramline stitches A&E applied.
I think a lot of nurses/doctors are prejudiced against glue and it should be used much more often than it is. Sterri strips are not necessary to support it because it is very strong, but they do no harm. I think the trick is to apply it skilfully. Staff training needed? Some people can obviously do this better than others, but that's the luck of life.
Best wishes for your daughter's good result. Sounds like there's every chance of a good one.