This is very much a "heart over head" or vice-versa scenario.
In all actuality ashes are essentially dust. Dust carries. When you're cremated, depending on where, they remove the jewellery you're wearing, you're cremated with or without your casket, you're scooped out with a shovel, and boxed up. In the crematorium not ALL your ashes are collected, some of your ashes remain on the shovel and are washed off, the crematorium is cleaned out. Aside from that, if you're scattered, the wind will carry the ashes. The critters will eat and run and play on the ashes. They might eat the ashes themselves, or inhale them. Logistically speaking, if you want to stay all together, don't be cremated.
My dad was cremated. I live internationally. I brought some of him back with me, and my niece took some ashes as well. The simple fact that part of him is here with me is, soothing somehow.
While I understand some people will "feel odd" about the idea of their ashes being split, you won't know if that actually happens or not. Sadly, or happily, it's not about you at that time. It's about closure for others.
So OP, do you feel you'll have closure if they're scattered at the family home? It seems your brother has some pretty strong opinions about it. If you don't, scatter the ashes there and grab a leaf with her ashes, or whatever and take it with you.