Does the child show signs of needing the nap? Does she go down quickly and easily for the morning nap? It will be harder to convince if she does. My daughter would have happily done 2 naps a day until past 2 if I had let her but I switched her over around 15months out of necessity due to my home daycare. My daughter was still doing two 2hr naps at that point, once I switched her she did one 4 hr nap. At 25months she still does a 3-4hr nap (plus 12hrs at night). She NEEDS sleep to function.

It is YOUR home daycare YOU call the shots. Inform them that as of XX date ALL children will need to sleep once a day to allow ALL children time outside to play and to allow all your other enriching activities. Inform this mom that you will now start shortening the morning nap, by 15minutes every few days so that the last few days before the switch she only gets a 20min nap.

Do NOT force the parents to do the switch at home. Encourage it...but ultimately you have the child 5 days a week...they can do what they want the other 2 but the child will naturally start resisting it at home...let the child lead them rather than you try to force them. They will be less upset by the change if you don't force change on them at home.

Be matter of fact, be confident, don't waiver. Don't tell her this is what HER child needs tell her this is what YOU need. She may be offended if you try to sound like you know her child more than her (not saying you don't lol).