What is the difference between “この部屋の中で遊ばないでください” and “この部屋の中で遊ぶことはしないでください”?
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It looks like the first sentence is saying, “Please don’t play in this room,” while the second sentence is saying, “As for playing in the room, please don’t do it.”
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Hey and welcome on the community forums 
When it comes to the nuances, the second one is more indirect and softer. Therefore people will consider it to be more polite.
That is basically it.
I hope it helps,
Cheers! 
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