She sounds rather unimpressive. It's hard to tell if she's a pisstaker or just lacking in initiative and imagination. Although the glowing references suggest the former - she feels like she has a cushy deal with you and she's milking it as much as she can. I think you need to have a performance review with her, spell out what parts of her duties she does well and what she falls short on and how she needs to improve. You can use the opportunity to clarify what expenses are covered in the role and what she needs to fund for herself.
If she doesn't improve because she either can't or won't then you'll have to make a decision on replacing her or if you can get your daughter into nursery and if you can then manage without a nanny.
it is possible that she was once much better at nannying but for some reason her performance has dropped. This happened with our part time (live out) nanny who worked for us for over 14 years. For the first few years she was fantastic, very high standards, lots of extra value stuff (she started teaching eldest to play piano etc.) I felt so lucky to have found her as my career - which went from strength to strength - would have been a considerably pared down version without her. My kids were in nursery but the arrangement was that she'd pick them up mid afternoon 2-3 times a week, take them home so they could chill out, she'd do homework with them, make dinner, play, do bathroom and get them into pjs. On those days I was able to work later/catch up and come home for cuddles and stories - everything else was done. She was wonderful. I did pay her well and gave Christmas bonuses and pay rises whenever i got one. If she was Ollie took holiday or her car broke down and she couldn't work, I still paid her.
Over the years though she got gradually lazier and sloppier. I did give quite a lot of leeway because she had personal problems which were very challenging. Her second child was diagnosed with autism, then she had a surprise third baby, a few years after that she then left her husband, was housed by council, then landlord sold up, went back to husband (who'd lost the former family home and was living in a caravan) so we are taking very challenging stuff. She was desperate to keep the job as she really needed the money ... But she just didn't seem much good at it any more. She kept dropping things from her role without discussion i.e. She stopped doing baths and put toddler to bed grubby. One of the days she was supposed to drop eldest at Cubs but he told me rather than taking him to the door she'd drop him at the park entrance and he'd have to walk there alone (in winter months it was dark).
She would make dinner at our house for her, her two younger children, and my youngest then just started to leave all the plates, pans etc dirty and dumped all over the kitchen for me to deal with. I d ask her to at least put the crockery and cutlery in the dishwasher but she'd giggle and say she "forgot". One of her kids seemed to have permanent loose bowels and if arrive home to find at least one of the toilets splattered and needing to be cleaned. It started to feel like she made life harder not easier. I did think "at least she takes good care of little one". But then my eldest - by then a teen- told me that she just sat in the kids tv room in her phone and ignored my little one and her own. Then our builder/decorator asked if I could have a word about keeping the kids downstairs while he was painting upstairs as they kept rampaging around, knocking into wet paint etc. I did but not much changed. I started to think I could manage without her and pay eldest some babysitting money instead but when I stated to discuss it she got very upset about how she'd manage.
Then covid/lockdown hit which kind of solved the problem! We now both work from home alternative days permanently. I paid her in full for six months then let her go, very politely, and sighed with relief. The kids sort of missed her but in a wistful way remembering the early days when she was a fab nanny.
Sorry what an essay! What I mean to say is if it's not working fur you and you can't get her to improve, you need to look at the alternatives.