If I'm getting the timeline right it sounds like this started either during or just after her brother's illness. This suggests it's linked to attention. The middle of the night may have been the only time she felt she was getting mummy and daddy to herself and this is now habit. There is nothing the doctor can do, it is simply that you need to break the cycle.
Firstly as others have said the middle of the night story needs to stop, it will be over stimulating her and making her brain think it's time to wake up. It's straight for a wee then straight back into bed, quick kiss and then back to sleep. Any fuss or getting up needs to be dealt with by firmly taking her back to bed with a calm, "it's sleep time now, I'll see you in the morning". This should only be said once and then nothing, no eye contact, no cuddles or kisses just put back in bed and then you leave and go back to your own bed. Repeat as necessary if she gets out of bed but ignore all calls for attention. She doesn't really need her daddy/mummy/a drink/another wee etc. it's all for attention. Your partner needs to be strict with this too. No doubt the first few nights will involve screaming and crying, possibly waking her brother but once you are through this she will realise night time is not attention time and she should start sleeping and self settling.
To make up for the loss of attention at night you or your partner could try making some one on one time with her during the day, playing together or something after school. That way she is still getting time with you on her own.
Good luck with it, I hope you manage to get it sorted!