Ilr got dependent child born outside uk

[Europeflower]

Asking on behalf of a friend. Any input will be appreciated.

Can an under 18 child obtain ILR as a dependent of a single mother who is applying for Ilr via domestic route?
The child biological father is in the U.K. with parent visa but the child lives with the mother who is applying for Ilr dv (as her new ex husband was British).
The guidance say she needs to have sole responsibility or the child normally resides with the parent with/applying for Ilr. Is this true?
The biological father is in the U.K. and sees the child occasionally. I know sole responsibility is important for entry clearance but is it the same case for kids already in the U.K.?

[zimba]

Children born outside the UK follow the immigration path of the less privileged parent unless:

their other parent is dead or
you have sole responsibility for their upbringing or
there are compelling reasons why they should be allowed to stay