I totally understand how you feel. My kids refuse to nap too. Both my older boys dropped their noon nap by 3. I gave up forcing them to sleep unless we have dinner to attend at night because it just takes way too long. Sometimes by the time they nap, it is time for them to wake up. All the time wasted when we could have done something together (plus my sanity!!) . So I decided to let them sleep when they feel like. My older boy who turns 6 in Nov is more sensible now. If he is tired in the afternoon he will let me know.
There's really no right or wrong in this whole nap thing. Every child is different. My younger son sleeps less than the older one despite whatever methods I try. So don't be too hard on yourself.
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mother of 3 kiddos