In my WA State condo, a Board president can make no rules about anything. Decisions need to be made by the Board, not an individual Board member, at a duly called meeting at which a quorum is present. Check your Association's governing documents.

In our docs it says the Board may make or change rules as may apply to certain situations. An example of this would be when our Board changed the rules for renting units which protectes the on site owners. If this was done it should be registered and owners should be given a copy. 
If you have a pool I could see thie parenting for children under 12 being necessary. Are there very young children, say a 3 year old, playing outside by themselves? Lots of "are there's" to be answered before you get a real answer.

I have a question: what do other HOA do with regards to deciding how to handle rentals. We have a set limit of rentals, and when one rental sells, what do other HOA do to decide who gets to have a rental next? 

Fair Housing--no discrimination, race, creed, disability. Service Animals. Also HUD has something to say about animals.

Regarding a HOA making a rule that states something to the effect "all children, 12 and under, are required to have adult supervision to play on the common areas." I do not believe that this rule would violate any federal law. However, you need to check the laws of your state for a definitive answer. A review by an attorney would be preferred. 
 
By having such a rule, the HOA may be exposed to civil litigation. 
 
My suggestion would be create a rule that would put responsibility for the safety and well being of children playing in the common areas on the parents or guardians. Something like: 
 
"Our common areas were not designed for 'child play'. The parent or guardian is solely responsible for the safety and well being of their child when that child plays in the common area. In addition, the parent or guardian is responsible for any common area damage incurred as a result of their child playing in the common area and will be billed accordingly."

Mary Pat Ankerson: 
 
You need to open a new topic. 
 
To do so find the red help button at the right edge. In the text "Can't find the answer you're looking for? Ask your question here and we'll post it in our blog." click on the word 'here' and you will be able to open a new topic for your question.

What does Federal Fair Housing Acting mean to condo associations? 
Nothing.. The states and the feds have no funds to enforce the 12,000 laws, rules and regulations, unless it is something particularly egregeous. 
Talk to the president on the phone for starters. 
If he tries to enforce some unenforcable rule, challenge him in public. 
God helps them that help themselves.

Yes, the rule is illegal. This is from a HUD publication:  
 
"Did you know that federal law makes it illegal for housing developers, landlords, and even homeowners associations to deny housing to families with children or to place unreasonable restrictions on children?.... 
Rules Cannot Unfairly Target Children 
Many parents are unaware that it is illegal for landlords to make rules specifically against 
children. For example, a landlord cannot forbid children from a common area that adults 
are allowed to use." 
 
and this: 
 
"The Civil Rights Act of 1968 (Fair Housing Act), as amended, prohibits discrimination in the sale, rental, and financing of dwellings, and in other housing-related transactions, based on race, color, national origin, religion, sex, familial status (including children under the age of 18 living with parents or legal custodians, pregnant women, and people securing custody of children under the age of 18), and disability." 
 
You can complain using something called the "Housing Discrimination Complaint Form". You can google it.  
 
However, I would recommend discussing all of the above with the board before complaining to HUD. Give them a chance first.