DH and I walked in and down the aisle together - we'd attended several weddings in the year prior to ours and both absolutely detested the crappy, cringy bit where the groom stands alone at the front and some "comedian" (in one case the vicar) feels compelled to loudly make jokes about the bride having changed her mind. Wtf is that a thing? I also absolutely hated the whole concept of being "given away" like an outgrown coat or an unwanted pet, and the cliché of everyone looking at the bride and making set piece comments about how she looks (no matter what she looks like).
DH and I had lived together, hundreds of miles from either of our families, for three years before we got married and owned a house together, it seemed absolutely fake and theatrical and wrong, to us, to do anything except walk in together.
I understand pretty much nobody agrees though - people like tradition 
We gave my dad another conspicuous hosting role and he was very much involved - we have a good relationship, which of course is why I was able to explain to him that I didn't want to be "given away" but wanted him to do something more important to us on the day.
I wouldn't choose one brother over the other in your position unless you are much closer to one, or one is older or the same age as you and the other much younger. Asking your mum is obviously completely fine as she brought you up!
You mention having children of your own with your husband to be though - perhaps both you and your husband could be given away, by one of your children each (or two each, or other distribution of roles to ensure fairness!)
Being given away when you already have children together is slightly shutting the stable door after the horse has bolted anyway 