Ahhhh......you can taste it, cant you......
But seriously, if you're more comfortable on your commuter,ride it. If she's talking you (a beginning "racer") into a tri that allows relays, my guess is that this isnt a hardcore race. You wil see all kinds of bikes there from mountain bikes to roadies, commuters and hybrids.
And keep the basket! Last year I did my first supported ride on my heavy Trek Navigator complete with basket on the front! Later that summer, I rode my commuter (sans panniers) with my basket on the rack. This second ride drew many stares and comments as most people were on road bikes - "i cant believe you're riding this with flat pedals!' And "nice basket!" I know they were all jealous of my basket and wished they had one...