For those who do not already know what a "frame challenge" is: What's a frame challenge?. However, I think the answer to "how do I address this as a father" has a wide variety of valid answers, many of which may consist of what some might consider to be a "frame challenge". If you set out to "fix" your daughter, then your own point of view might really be the thing that needs fixing.
Does your daughter have exposure to other extended family members (your wife's family, presumably) who do not speak English with her?
Just as a reference point, have you read any material about "strong willed child"? It sounds like your first child has raised your expectations and your second child is quite different. Different children will need different techniques. You say you've "tried all techniques I've read", but we don't know what you've read.
You say you had your phone "locked down" for a video chat. Does that mean this was the first time you did a video chat with Grandma with your daughter? Or was this the first time your daughter got to hold/manipulate the phone while on video chat with Grandma? Put another way, was this your daughter's first video chat ever? It's not really clear the way your question is written right now.
In some cultures, what your wife is suggesting is exactly what happens when women give birth in that culture. For example, see For Chinese Moms, Birth Means 30 Days In Pajamas. I don't know what your wife's cultural background is, and whether it's different from yours, of course.
This can depend a lot on local cultural standards. Which country or city are you referring to?
Does your husband know he is not your daughter's father?