A couple of thoughts here.
As one who's gone through the mill in Australia and worked many years in the outback etc and then converted the ATPL to a JAA one a couple of years ago I have some thoughts.
The so called "self improver" route, that is instructing and the like may not look nice on paper as it's comparatively poorly paid is actually a lot of fun. You actually learn how to fly and what it's about versus tapping away at the FMS and following the magenta line. The guys we have that's come through the GA route flying king airs are excellent operators and are generally more customer focussed than those who have only known airlines and the locked cockpit door.
I wonder if your daughter just wants to become an "airline pilot" versus a "pilot"? The VLJ market will have some very tough competition from Netjets (who use a CS reg = Portugal) and other companies. With the bizjet market, you're more of a multi tasker in comparison to the airline pilot.
GA will teach and condition you to programme changes, get you used to sorting out luggage and catering, customer relations and other things that is part and parcel of the GA/bizjet world. Also gives you a better insight and experience to deal with the various issues airline guys deal with too. Can't have too much experience.
So, I'd ask your daughter exactly what she wants with respect to a flying career and does she know what the bizjet world is about? About her A levels? Let the airlines decide whether or not she's got enough. The airlines can't say "yes" if you don't apply. At 20 she may need to bring something else to the table of course, and she has a lot of time to absorb the inevitable recruiting down turn that follows a hiring boom.
2 licenses are better than 1. The FAA license will open up some doors in the bizjet world but the FAA and JAA license will open up even more.
Have you considered Australia? There's an Australian flight school in Perth (Oz Perth, not the Scottish one) that runs a JAA course and the IR is done in the UK in Cranfield? The FAA license isn't that hard to gain if you already hold another national license. (I currently hold an Australian ATPL and a JAA ATPL and a permit from the FAA to fly an N reg Hawker).
I hope this helps.