As so many have already said - just ask - but keep on asking as time goes by!
I remember my own mother being surprised that I took so well to motherhood myself. She herself had been a young mother who, by her own admission, rather regretted not having the years of independence I did before starting a family.
We didn't live near to each other, either.
And she was used to my being able to cope with new challenges.
However, this did not mean that more offers of help wouldn't have been welcome, especially when the chips were down. I suffered a miscarriage at one time, and a serious physical illness at another, leaving me incapable for some months of looking after myself, let alone a young child.
Just keep your ear to the ground. Even if she doesn't always say yes to your own offers of assistance, they will always be appreciated.
And always tell her what a brilliant job she's doing!
Being quizzed by chemist's assistant in Boots.