Can my kids be bilingual?

Losing the battle in my 用心良苦 attempt to have my kids be effectively bilingual!

So we've been investing deliberate efforts since Yx was young, speaking to her in Mandarin as much as we can. It helps that she was under the care of both yeye and nainai who are primarily conversant in mother tongue. Well, not 100% pure Mandarin, as there are times when we mash in a few English words (most of the times nouns and adjectives), but mostly and mainly Mandarin! We even teach her multiplication tables in Mandarin, and borrow 1-2 Mandarin books from the library each time. 

But recently, I observed she's beginning to think and respond in English... I guessed she's been exposed to too much of it at school and on TV (Wiggles, Peppa Pig etc).  Well I have nothing against her English because her spoken English is really very decent for her age! It's just that gradually she's switching from more Mandarin to English... when she's nervous she even speaks with an outlandish Peppa Pig slang it hurts my ears >.<

Discussed this observation with wifey (who has a rather good command of spoken English) who didn't feel it was a big issue - she'd rather Yx be a master in English than speak typical broken Singlish like most Singaporeans do. My counter was that school-goers will be using and hearing English 95% of the time in school any way, furthermore it is easier to pick up English than Mandarin; hence we should practise Mandarin at home... this discussion didn't reach a conclusion yet and it doesn't help that wifey is more comfortable and intuitive in English... =/ So both of them would be exchanging convo in complete English sentences like in an English class. I've observed that Yx would speak/ask/initiate to wifey in English... And beginning to do the same to me.

Really don't want my kids to turn out to be uncomfortable in Mandarin in future. It's been the trend in kids (and teens!) these days. English fi-li-fey-ley but mother tongue is like alien to them, worse, they even admit with arrogance that it is! Reminds me of my experience with Yx's cousin, J who is 5 years+, he speaks English at home and attends Berries:

Me to him: "你吃饭了没有？"

J stared blankly at me, eyes wide open and afraid to blink. He looked right at me like his brain was processing what I said but he doesn't know how to respond; he uttered nothing and only mustered a tiny tiny nod, the look in his eyes reflected that he hoped that's the right answer to my question.

SIGH!

Readers, if you have any tips pls share some guidance!