Mine is almost 3 some days too. I have trained all my kids that even if they wake up prior to the 2 hour min they still lay down until I come to get them.
It's for their benefit but it's also for mine.
Parents don't understand that we are not a centre where there are multiple employees. It's just me and 5 kids. I need my break!
I would leave him to cry it out. I wouldn't keep going in to check or allow him to have books.
I have kids who don't sleep at all at home and their mom gets them every time they make any kind of noise. Here, they just lay there... because they know I'm not coming!
In my experience it takes about 3 weeks for a child to "get it" in my care.
I would simply tell the mom (if she brings it up again) 2 hours is the min. Kids need their rest, you have a full day and they need to rest. You also need to rest and need the break in order to set up for the afternoon activities.
However, if mom doesn't mention it then I wouldn't. Let her bring it up. Your house, your rules.