Legal separation with no will isn't an automatic you and your brother. Mom could contest any such judgment and credibly get it all.

A lake house is a far better investment than anything you would do with the money while still living at home.

So, you're talking about fighting with the provider of your living conditions, over money you'd likely lose anyway, over an expressed wish to invest in an equity property you would receive a half share. You'd also have access to a safe place in transitional periods. So long as you never comingled, you likely couldn't lose it in divorce, and definitely would always have access if on good terms with your brother.

I'm boggled.