You would need to read the easement to make sure you are within your rights to put the play yard in.. At a later date the HOA might require you to move the fence back. Is there a possibility that they will release the easement since they don't plan on using it? That would enhance your value. On the last question, the answer would be subjective and would depend on your local market.
The answer to your question depends on the wording of the easement. If the easement is non exclusive, you and your kids can play on it. Fencing easement land or constructing a play yard on easement land with association approval gives you a license to use the land. Licenses are personal, can be revoked at any time by the association, and do not pass with the title to your land. Therefore, exercising the license by using the easement area should not increase or decrease the value of your property. If you are unsure of your rights with respect to your property and the easement, you should consult an experienced real estate lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
The wording of the easement will dictate what you can and cannot do.
Improving the appearance of your house can increase its value which in turn can result in higher property taxes.
I am not a FL attorney, laws vary from state to state, therefore you should always consult a local attorney.
If this answer was helpful, please mark it as helpful or as a best answer. This answer is for general education purposes only. It neither creates an attorney-client relationship nor provides legal guidance or advice. The answer is based on the limited information provided and the answer might be different had additional information been provided. You should consult an attorney.