Hi OP, I understand where you're coming from.
- Brother complained about your daughter/his niece not knowing him well.
- You explained that it's because he rarely sees her.
- You believe this is because he doesn't make enough of an effort.
- You offered to set up a mutually agreeable time to visit so they can see each other.
- He declined.
IMO, you have done everything you can do. The ball is in his court now. Drop the rope and don't feel guilty.
If he wants to foster a better relationship with her, he can. If not, he's just complaining to complain and he sounds like a big baby and a pain, TBH. Your whole family does!
I have family like this and I just ignore them and do my own thing. I spent years trying to bend over backwards trying to please them and nothing was ever good enough. I finally realized they just liked to complain and be miserable.
So, now I do do what I want and if they (my siblings... as I've cut off my parents) want to see my kids, they'll make it a priority. If not, oh well. They can bitch to each other about it, I don't care, but they'd better not bitch to me about it if they want to stay in my life at all.
Things are so much better this way!
Just concentrate on yourself and your own chosen and created family and don't let your miserable-sounding family of origin drag you down. If you have a party or feel like extending an invite to your brother/family to do something together, go ahead, and it's up to them whether to accept or not. If they in turn extend an invite to you, it's up to you to decide whether it feels in your schedule or not.
Not all relationships have to be fostered. I don't see what a 30 year old single guy living at home with his parents would have in common with a toddler or what he would want to do with her. But if he does, cool.
I have four siblings and two of them are much younger siblings I wasn't raised with (like, 20 years younger... but I'm 42) and they are pretty good with talking on the phone to my kids and being fun aunt and uncle... my younger sister now has a child of her own who is around the same age as my youngest... so we talk when we can but they live 2,000 miles away and it's impossible for me to see them because they live with my dysfunctional toxic abusive parents whom I've cut off. There's also just a limit to how much my 21 year old brother can really "care" about any little child since he's young and single and carefree and stuff, so I try to have realistic expectations.
As for my other siblings, well, even though we're closer in age and they have kids around my kids' age, I've realized that unless I put in a lot of effort and/or did everything THEY wanted to do the way they wanted me to do it, I rarely see them, and that's fine with me because it shows me just how little they care unless it's convenient for them, so why should I care if it's not convenient for ME? I have no interest in going near my parents' house or even my hometown again and all my siblings live in or near my hometown and our parents.
So, if they want to see me, they come out and we do a joint vacation at a mutually agreeable place and time, because I don't want them in my house either. (They're very judgmental and entitled and my home is my sanctuary and I don't want them causing trouble for my husband or kids or me. Nor do I want them knowing too much about my life or they'll go gossip to my parents who will try to get to me more after I've cut them off.)
It's been like 4 years since I wised up and stopped going out to visit my family of origin (at first it was due to Covid, then a cut-off of my parents that happened nearly 2 years ago) after YEARS of flying my whole family out there 2-3 times a year or letting them come whenever they wanted and bring all their drama to us. (Mostly me going out to them though, which they were always demanding/entitled/guilt tripping about.)
And do you know how many times I've seen any of my siblings since then? Only once, when my sister who is closest to me in age came out to a neighboring state for a joint vacation. That was over a year ago and I have no idea if it will ever happen again because she made it so difficult and made a big fuss over the fact that I wouldn't let her whole family crash on my living room floor and dared to ask her to stay in a hotel despite the fact that she and her husband are loaded so it's not like they couldn't afford to.
We can only really change OURSELVES and our own reactions to people; we can't change them or their actions. We shouldn't concern ourselves about what they think or say about us because our opinion of ourselves and doing what's best for ourselves and our own family is what matters. I vowed to cherish and support my husband and put him first. I willingly brought my children into this world and have a duty to support them and put them first as their mother.
I did NOT ask to be born into my dysfunctional family of origin for my parents to control and own and abuse. I did not ask to have my siblings and have a whole toxic family system. I have no duty to put them first or do anything for them. In fact if I were to do that to the detriment of my own well-being and my own created family's well-being like I used to do, then I would be being derelict in my duties towards myself, my husband and our kids. And I would be continuing the toxic family system.
I feel sad that I'll likely never see my youngest siblings again since they are so enmeshed with and dependent on the parents who abused all of us to the point that I had to cut them off. I'm sad that my parents are the one who broke my family of origin like this and therefore the rest of us have to suffer.
But I'm not about to jump through hoops to see people who are still caught up in that system and want to drag me back into it. I have learned through LOTS of therapy and reading how to have boundaries and do what's best for me. Those who love me will find a way to stay in touch to whatever degree possible. Those who don't can't just stay out of my life because I have no time, energy or focus for people who don't want to make any effort and complain about ME not putting in enough effort even though I used to all the time and it made no difference.
So, just focus on your beautiful child and spouse and stop worrying about your brother and your parents. Who cares? They sound like they're a mess and like your parents have enabled this golden child/scapegoat dynamic and enjoy pitting you against each other. Don't let that define you. Step away from all of that that you can't control and let them have each other while you focus on what you can control.
IMO you have done everything right except that you still seem to be catering/pandering to what your parents want too much, and still letting what your brother says/thinks bother you too much. Free yourself of that unnecessary anxiety so you can have a happier life. :) If they really love you they will make sure to make an effort and let you know.
And it could be that brother is just caught up in his own life and doesn't understand why a little kid wouldn't know/love him when he never sees them... so all you can do is explain that it's because he doesn't know her and offer some times you're free to get together in a way that works well for you (I would recommend it being separate from your parents as that sounds like a big toxic mess you don't want to entangle yourself in and get caught up in all the triangulation and enmeshed family system etc.) and see if he wants to come. It sounds like you've already done this so rest easy that you've done your part, and see if he ever comes around to doing his. (He probably won't and in that case, you and your daughter don't need him! All she needs is the love of her parents and you're giving that to her. :))