the female Country singer who sings a song with some of lyrics I hope can be like that my son...?

The country singer you are referring to is Kelsea Ballerini. The song you are thinking of is "The Other Girl". Here are the lyrics you mentioned:

"I hope he can be like that for my son one day

The way you were there for me through everything, so effortlessly

If only you could see the man he's grown to be

How you'd be so damn proud I know it"