I voted YABU, based on I got the impression that it was your partner who gave birth (please correct us if we're wrong).
YABU because your partner is going through serious changes to her body. She'll be swollen, in pain, and her hormones will be all over the place. Right now, she only wants to be in the company of people that she's comfortable with.
She clearly has issues with your mother, no one who has just given birth wants to be around an in-law that they don't get on with.
Waiting a month for her to recover from the birth, baring in mind it takes 6 weeks to establish breastfeeding too, is more than reasonable. My own mother only met my children when they were 3 weeks old, and my Dad only met them when they were 3 months old. And I have a good relationship with my parents, we just don't live in the same country.
I do feel that it's unfair to rush your partner when she's very vulnerable right now. If she is the one that gave birth, she's the one who has gone through the massive life change, much more so than you have. Therefore, in my view she gets to give the go ahead on how soon various people come to visit.
I see some posters have suggested that she's controlling, I disagree. It's important for your post-partum partner to feel comfortable right now, she's protecting her comfort and new found role as a mother. If you as her partner push her on this, or just take baby to meet your mum without her, your partner will resent you for not supporting her. Please do not separate newborn baby from mum as other posters are suggesting, that is the ultimate cruelty that a partner can do to their post-partum partner.
Your mum should be respectful and wait until your partner is ready and one month certainly is not unreasonable.