please I need advice

I got my indefinite stay last year, I live with my partner. We have 2 children together, 1 and 4 years old, both born in the UK. My partner has no regular status, she is illegal. 

Please what are my wife's chances of regularising her stay

Try and register the children as British Citizens first, then she will be able to apply under the immigration rules and explore exception 1.

Was the youngest child born before or after you were granted ILR?

Good point Amber. Thought the children were 2 and 4.

I must have misread the 2 children for 2 and 4 years.