Around here a similar hurdle for beginners is their first 'Strait Crossing'... depending on where you do it it's a 15-20 nm shot across the Strait of Georgia - sheltered but still a potentially rough ride if the weather turns on you - it can be quite nasty.
It's typically no big deal.. in fact in the past 35 years we've probably motored across in calm many more times that we like, and many many more times than the few 'white knuckle' crossing we've had. Nevertheless it's that FIRST time that can be psychological hurdle...
I suspect your wife is in the same place.. and the trip to Catalina is an open ocean one. Give her time.. she'll come around.
Going yourself with a good weather window on a well found boat should be fine.. have you considered the mooring situation at the other end from a singlehander's point of view? When you say 'one day' are you talking there and back? This could be a long day... do-able, but for typical casual cruising a 30-40 mile day is a longish one. Also, it seems to me having sailed there you'd like to stop and explore... necessitating an overnight stay.
But a non stop solo adventure would be something to reflect on too....
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)
1984 Fast/Nicholson 345 "FastForward"