That's really hard for her - she's having the same experience as she would if she'd only recently moved rather than the experience of a child born in the country.
Tbh it does also explain why you still feel as though England is home.
I know "integrating" is pushed and it's tempting to push back, but if you're realistically likely to stay permanently and send your child to local school for the next ten plus years you need to be 90% integrated otherwise you're making your child's life harder than it needs to be. I arrived here pregnant and with a small toddler only knowing a few phrases but really had to throw myself into picking up the language and building a local (not expat) network as we're not in a city. This was incredibly, intensely hard but I must say paid off as my children were absolutely (age appropriate) native speaker fluent before they even started preschool age 3 and teachers were always surprised to learn they were bilingual.
I did it more by luck than judgement so I'm not taking credit! However I've since met people living in English speaking international bubbles in the next city who's children have not coped with local school and had to be moved to extortionately expensive international schools. It's much harder for children whose lives are 90% in English to cope in a school system not in English.
Adults who's social networks are all international also seem to remain in limbo identifying their country of origin as "home" unless they're very wealthy expats on the "circuit" - which is a different experience again.
I think, to be honest, you might have hit a "crunch" point where you have to stop sitting in the "just visiting" international bubble and decide to throw yourself properly into integrating (local almost everything especially for your child, especially doing everything to cultivate local non English speaking friends for her) or return to England. Unless you can afford to be a full on "expat" and pay international school fees.
It's not really fair to keep up the hovering type of not really sure whether you're staying so not really integrating thing once you have a child in the local school system.