These cons are, um… No offense to your mom, but she’s wrong. There can be wealthy and/or snobby people at almost all private elite colleges. Brown isn’t summer camp. It seems you feel you will be happier at Brown, which counts for a LOT.
You sound much more interested in the Trinity/Columbia program and you seem to love history. As far as Trinity throwing you in the deep end, yes, you will be more self directed there. But Dublin is a fun, lively city and you won’t lack for things to do. They expect students to be able to handle themselves and their studies.
Both Columbia and Brown will open doors for you so I don’t think the “prestige” factor matters. But if you are really concerned, it seems your degree is actually awarded by Trinity. Is that right? Trinity will not have as much name recognition in the US. If you are intending to stay in Ireland/UK it’s possibly a better name than Brown or Columbia. Outside of the US, people mostly know the household names i.e., Harvard and Yale.
Go for the place you think you will be happiest at.