As for Andrew and the present time - hopefully he will voluntarily stand down from his current position and spend some time trying to re-establish himself but doing what - who knows - he doesn't really have anything going for him and what charity would want him?
Well, in my dream scenario, Sarah would become CEO and/or spokeswoman for her own charity for disadvantaged children/youth--something like her Children in Crisis charity, but more based in Britain. There would be drop-in centres for youth across Britain, and she'd spend a few days at each one, interacting with the children. The rest of her time would be spent speaking at schools/community organizations about childhood abandonment, the effects of divorce on children, etc. Sarah would learn a few key points about the best ways to help children cope with these issues, and she'd make sure to hammer them home in each speech. This would be her primary job--no more forays into Oprah or other reality TV shows.
Andrew would drum up financial support for the charity by visiting various businesses (much as he does now, but this wouldn't be for the UK, it would be for the charity). Just as now, most of his public duties would consist of his work for the charity, although he would still peform a few official royal duties.
The girls could get jobs there as well!
Andrew and Sarah could then remarry while somewhat avoiding the problem of Sarah's re-entry into the royal family. While they'd have to be together at major family gatherings, royal life will start to revolve around Charles' immediate family, and Andrew and Sarah wouldn't have to spend too much time with the other royals. Andrew would perform some royal duties without Sarah at his side; the rest of the time, they would work together at the charity--Andrew drumming up financial support; Sarah drumming up psychological support.
I can dream...
Back to reality: I think Andrew will never step down from his UKTI job voluntarily unless he has done something HUGELY incriminating, and knows he has no choice. I think it is a self-esteem thing for him--as Iluvbertie says, what would his public role be without this job? He is the second son, and will get pushed further down the line as William and Harry take on more public duties.