OP, if you want your niece to be part of your life moving forwards then you need to build a relationship with her mother, separate from her relationship with your brother. You don’t have to be best friends. But if you treat her with respect and consideration in this situation it is going to go a long way to cementing a good relationship between you two, as opposed to her feeling like an after-thought or an inconvenience.
You will appreciate that attending a wedding, you want to look and feel your best- nice clothes, hair and make up done etc, especially when meeting new people. At 3m post partum the mother may not have suitable clothes that fit, or even if they do fit they’re not suitable for feeding. No time to get a hair appointment or do make up, having to wear a nursing bra and breast pads, worrying about boobs leaking, worrying about baby doing a massive poo and needing an outfit change. Worrying about baby crying during the wedding, the first impression people will get.
You need to speak directly to the mother (don’t go through your brother). Explain that you’d love to have your niece at your wedding and that you’d like to support her to feel comfortable in making this happen. Would she like to be a wedding day guest? Would she like to bring a friend/her mum/someone for support? Would she like a room to stay over in the hotel/venue? Would she like to come, not be a guest but instead come in casual clothing and you arrange for the venue to have somewhere for her (a hotel room, a lounge bar) where she can sit and chill, and you brother can come and get the baby and take her around the wedding guests, the mother can bring a book or a podcast and you can arrange for the venue to give her a meal, drinks, snacks, and when the baby needs a feed or gets fractious or needs cuddles with mum then your brother can bring her to her. She could stay as long as she feels comfortable but there’s no pressure for her to have to meet anyone or dress up or be formal, but she’s on hand and comfortable.
Do consider that if it’s too much arranging for you and the venue or if the mother doesn’t feel comfortable, then you may have to say to your brother sorry, no, it’s not practical to have the baby at the wedding. After all, it’s your wedding, not a baby-meeting event. If family want to meet then baby they can drive and visit your brother on one of the three times a week he has her.