Mia napped fine on Saturday...but not on Sunday. I was napping and my wife went into Amelia's room a number of times to find her standing up and not laying down. My wife slapped her hand and said "Lay down!"...Mia immediately laid down. She understands the command.I disagree, respectfully, with the notion to let the child play. At first I thought the child didn't need the nap but then you described her behavior without it.
For what it's worth, we have trained our children to know what it means to "go to sleep" by about 12 months. A child that age can be "forced" to go to sleep if they are tired in the sense of disciplining them to lay still for about 5 mins.
I don't know why it works but a stern male voice "Go to sleep" does. In some circumstances, I have also held a wiggly, screaming child still until they are literally exhausted from the struggle. It might take a few tries.
Also, consider that, at this age, the child might be teething and that could affect their sleep and some Tylenol might help.
I woke up and saw I was alone and asked my wife what was going on...so I told her to let me go in the next time. Within 5 minutes, Mia was up again. I went into her room. Bellowed out her name, slapped her hand, and sternly said "Lay down!", then I laid her on her back myself and put a blanket over her. She cried for ten minutes (rubbing her eyes from tiredness) then proceeded to sleep for the next 1 1/2 hours
When she woke up from her nap, she made her usual noises...when we went in to get her...she was laying down. I asked her if she'd like to get up...she kept laying there. I reached for her, and she extended her arms...she wasn't sure if she was allowed to stand up! I found that amusing.