What about individual no drill blinds on each window? they clip inside the frame minimising gaps at the bottom.

Agree with you re: roman binds - they do look wonderful but not so practical for either daily use or a child's bedroom.

Not sure what age your daughter is or if you require total blackout for sleeping purposes which will impact on your decision.

I love the window over looking the garden (and maybe a little jealous) and suggest wood type venetian blind in a light colour and dropping to the sill.

At first I thought Roman or roller blinds but they may let too much light in at the joins. Shutters may be another idea but an expensive option.

Blackout Honeycomb blinds might be an option. There's only a tiny gap between the individual blinds so they're quite practical for bay windows - as in the photo. Joy

We can offer made to measure Bay window curtain poles. It looks like you could easily use ceiling brackets but custom brackets are possible and it could offer returns into the room allowing a wonderful curtain that doesn't then have to be floor length. Our passing brackets offer the chance to allow a pair of curtains to draw past easily.

https://www.nigeltyas.co.uk/made-to-measure-bay-window-curtain-poles.html