Switching from Tier 4 to Private Life Route

[Newbee123abc]

Hi,
We are non-EU citizens. I will be finishing my PhD soon and my wife is my dependent (with Tier 4 student visa). I am presently working as a tutor in a college. By April next year, I would have been 10 years in the UK. My wife and I have a child (aged 10) who have been living in the UK continuously for almost 8 years, we would like to apply for the Private life route for remain to stay. However, we also have two other children (5 and 1 born in the UK). I would like to hear your view on this, as I understand that my older child has the right to apply under the Private life route. Do you think we could as a family switch to this route as my studies end soon?
Thank you for your help!