I believe there was a case in Fal about 15-20 years ago with a similar issue. Can't remember the resolve. 
 
maybe someone can do some research on it.

If your bylaws have a restriction relating to children you have to abide by that rule.

Is this a 55+ development? 
 
 
 
If no one under the age of 18 is permitted to visit longer than 3 mos then your children may stay longer but your grandchildren cannot if they are under the age of 18. In answer to your question, "Yes" the HOA can make them move!

Things we didn't think about before we moved to condo living. If times were better,I would be out in a minute, or if I knew then what i know now about condo living, I wouldn't have moved in You don't own anything but what's in between your four painted walls or do have any say so in so many things.

In a properly managed condominiuim the council of unit owers control. All major decisions are by vote at open meetings which in themselves are deliberative associations. Even small itgems such as waiving the reading of minutes is decided by majority vote of the assembly (ie the audience at the meeting) 
 
If your condo is being mismanaged part of the blame rests with you-the unit owner.

Mr. Adler, Your comment is not realistic, unless you have a dream team board. 
 
We have two condos. Our permanent home (condo) in IL. and a (winter)condo in Fl. If what you said in your comment is true, we have two mismanaged associations, who, do not run things according to the by-laws. When we tell the board we should have some say so in what ever they propose to do they tell us we voted for them, so what they decide, is right, or, if they are not following the by-laws, they tell us it's a matter of interpretation. So, if they think their interpretation is the right one, what can we do? 
 
 
 
Can you please tell us why we are to blame for how the board runs the place?

simole. You did not uindertake any action to force the Board to consider your votes on criticsal matters. The usual excuse-I was afraid of retribution by the building manager!A bully as the President of the Board is the usual cause of most condo problems.

Can the board do anything with two teenagers who have constant visiting from other teens. The mom is a single parent who works nights so it is the most popular place in town, no supervision. I once went to the unit because of the noise, 32 kids piled out. The halls and carpets have tracks leading to their unitand all the glass has their DNA. Is there a legal solution?

What do your bylaws say about objectionable behavior??

Call the police. It is a quality of life issue...disorderly conduct. There must be a noise ordinance in your town. Then report it to the prop manager so that they have a record of it. Our residents do this all the time. We were able to get student renters out because of all the police calls to that unit.