Real Estate Law
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Basically the first thing to do would be to read over your Bylaws to make sure that it has the language about the prevailing party being able to recover their costs of any legal action. Then if it does state this, you can contact a local real estate or civil litigation attorney to discuss how to proceed. But without getting an actual judge issued injunction against the Board ordering them to perform their duties in enforcing the Bylaws.
Another option you could also consider is actually suing all the owners who are renting their units. Any owner can sue any other owner if they are violating the Bylaws because the members and the Board both have the power to enforce them.
And yet another option, which might serve to end the problem long term, would be to get enough owner occupants together to vote them out and take control of the Board. Then you could enforce the Bylaws as written and presumably issue fines to the renting owners for their noncompliance.