The story reminds me of some of these "zero tolerance" stories that have been in the news lately--like the 6-year-old who was going to be sent to reform school because he brought his Cub Scout eating utensil to school.
The community can always vote on amending the HOA rules. It usually takes a certain percentage of homes (I think in ours it's 60%). However, I doubt they can say "we'll change it only in Kimberly's case." What happens when Mr. & Mrs. Smith decide they need to take in their 3 teenage grandchildren? How about Mr. & Mrs. Jones and their chronically unemployed 30-something son? Pretty soon the reason these folks bought and paid for their community is gone.
I’m betting the child has become a brat.
That said, looks like the HOA took too long to officially complain. Like squatter’s rights. They may end up having to grandfather her in.