You had a baby 3 weeks ago.
What matters now is what is helpful to YOU.
Your mother is YOUR MOTHER.
You wanted her help and support because she is YOUR MOTHER.
When your DH is off work trying to learn how to breastfeed, then his mother can come around and help him and your mother can stay at home.
This is YOUR home and YOUR time to bond with YOUR child and if your MIL is making you uncomfortable, then she needs to go home.
It is very nice of her to offer to help. But you are not finding her presence helpful, you are finding it oppressive.
And that's fine. You just had a baby and are in one of the most vulnerable times of your life.
If she's a nice woman she would not want to be there knowing how you feel.
This is not about equal time for grandmothers and anyone playing that kind of competitive bullshit when another woman has just had a baby has a fucking screw loose.
Do you feel able to ask her to go home yourself? Or would you prefer your husband to talk to her?