Just sharing what we experience here.

Our background: both family are cantonese speaking
My family: SK educated
Hubby family : Chinese educated
When we have this baby (1 and only for both side of family), we actually discussed and decided only to speak mandarin and English with him. As the family members didn't converse with each other in English, most of them speak broken mandarin with the child. Only myself speak English with him. But I do notice he prefer to converse in English, thou most of the family speaks cantonese/mandarin. End up I let him join SK. But what unexpectedly, now English has become his mother tongue, he hardly understand Cantonese and his Mandarin deteriorating.

I have a friend send his daughter to Cambridge English since kindergarten age, every year until now age 10. And the girl English have never improve, she even get so bored to study. And of coz, she in SJK. What we analyse, the kid may already get bored with tuition as it started too young.

TS, if you want her to improve in English. Surround her with English books. I bought lots of books to my boy.. No matter he read it or not.. even he trash it.. i never force him to read.. but a big shelves readily there. Let the child sing English song.. go for interesting English medium activities. Am not sure how alert are you towards her spoken English. You actually can correct her on the spot, if you notice some flaw.. using a friendly way. As young child have open minded to learn, but dun let them feel it is classroom. Let them learn as in.. they growing up.. is a daily practice to speak correct sentences.