Clearly from the text, sola scriptura, Solomon was very much predisposed to grant the request ... until he found out what it was. So the problem wasn't with the request coming through the Queen Mother, but with the request itself.
Adonijah was executed because the request was tantamount to high treason.
So I suppose the lesson that can be learned is, "Don't make treasonous requests of the King, even if you make them through His Mother.
Actually I think the problem was with Queen Mother Bathsheba. Was she absolutely clueless? What was she thinking? Needless to say, I'll bet that was her first and last request.