Part of the reason she stopped competing was that she wasn't as good as a lot of the rest of the British competitors at the time - she was very good but there were others that were better at the time. There are people who strongly believe that had Mark been in the team in 1976 instead of Anne (he was the reserve and in those days only four were able to compete at all) the British team would have won a medal - that Anne was the weak link in the team and really should have been the reserve.
What factored into her decision to deny her children titles was the fact that her mother would have had to actually do something, unlike for her brothers whose children were automatically titled from birth as they are boys and Anne is only a girl. She knew, from the example of Margaret's children, that they would move further and further from the throne so give them a chance to be untitled and been normal commoners rather than commoners with titles, such as Princess, Lord, Lady etc. Mark was also happy being a commoner and didn't want to be a peer and thus have a seat in the House of Lords and a potential role in politics.
