I could use some help with nap extensions. Please see my question below. Here is some background:

My son is 19 months old. He happily goes to sleep on his own for bedtime. In the middle of the night when he wakes up and cries (about once a night) he usually puts himself back to sleep on his own after a few minutes, and the majority of the time he goes down fine for naps as well (if he protests naps we do CIO with checks). He is not easily soothed back to sleep by us, so we try to let him do it on his own.

The problem is that he has been taking really short naps. Only one 40 minute nap a day on weekends when he's home with us. When he wakes up after 40 minutes he's crying and seems tired still. We've tried calming him to go back to sleep, and then also let him cry for 30-40 minutes after he wakes up but he just stands and cries. We know he needs to sleep longer for naps. He used to take one nap that lasted a little over 1 hour, which was on the short end, but was better than this.

It sounds like at daycare he naps a little longer, usually an hour or 1.5 hours, and then often stays on his cot resting, so he's napping/resting for the full 2 hours. When we travel he usually takes an hour long nap too.

He's been waking up early lately, but he used to wake up around 6:30am. We've been leaving in his crib until 6/6:15am and sometime he falls back asleep, sometimes he doesn't.

His schedule recently is:

Wakeup: 5/6am
Nap: 12:45/1pm- 1:30/2pm (at daycare they have him nap/rest from about 12:45-2:45pm)
Bedtime: 7/7:30pm

My question is - how do toddler nap extensions work? If he has already slept for 40 minutes for a nap, can we expect him to fall back asleep after crying for 45 minutes or longer?

I am usually the one on board for more of letting him work stuff out on his own (CIO with checks), but my husband has a hard time with it. Then that makes it hard to be consistent.

Apologies for the long post, and thanks so much for any thoughts you have!