Thank you, ladies!
I have offered for them to drop him off at 12:30 with no additional fees. I've told them that he disrupted the others at the 1:30pm drop-off time. I've also told them that I had to start keeping the little girl awake until he arrived and that she is exhausted by that time. (Poor girl).
I have figured things out. It seems that he doesn't like to share a room while sleeping. He was here alone on Tuesday, and napped without any problems in the afternoon. This week, he has been here full days. That probably makes a big difference too. He's also been waking up a little bit easier after the 1 hr nap I allow in the morning. I have him up by 10am. I aim for 9:30, but he doesn't always wake up very easily. At 10am, I pick him up and force him to stand on his feet.
I've also decided that I have a nap schedule. There are no exceptions during nap time. BUT If he is tired before nap time, he can go to sleep earlier, but he has to stay in there until my scheduled nap time is over. (He has been sleeping longer).
I've found in the last couple of days that he sometimes needs a morning nap, and sometimes doesn't. He definitely needs quiet time in a dark room though. Every morning at 8:30am, I change his diaper, wash his hands and put him in the playpen for a nap. Sometimes he sings to himself quietly, sometimes he falls asleep right away. He does not fight me on naps in the morning. When I go in at 9:30, he'll sometimes be passed out, and sometimes jump up excitedly to be taken out for a snack.
No matter what time he woke up from his nap, I still get him to eat lunch at 11:30am. By 12:30pm, he understands that it is nap time. I allow a little bit of play time before 12:30pm, if it does not take him the whole hour to eat. At 12:30pm, I double check his diaper (usually change it right after eating) and place him in the playpen. If he's slept in the morning, he'll protest. Eventually, he'll stop complaining and will sing to himself. By 1:30pm, he is usually asleep.
I never knew playpens had those velcro strips. I never tied them. I guess I never really paid attention to it. I found them on Wednesday after the millionth time of him taking off the mattress. I stuck the strips together, and he hasn't taken the mattress off since. He hasn't even pulled the sheet off.
My other dck hasn't reallly been here much this week, other than Monday and for a brief period yesterday. He seemed to be more upset when she was here during nap time. I've started training them to sleep in the same room. The other dck actually sleeps better in the room with the 23 month old. The 23 month old seems to be getting used to her, but seems to give me the hardest time when she is here.

As far as the parents are concerned.... I am a bit timid when it comes to making suggestions on how to raise their child. I have no problem telling them certain things. Lately, I've been repeatedly telling them what kind of day he has had. Hopefully, this will be a hint that something needs to be changed. I tell them that he is tired, cries a lot, rubs his eyes, sleeps way more than he used to. He is only happy for the first half hour after arrival. Dad's response was that he is always cranky when he wakes up. I replied: I agree that he is cranky when he wakes up, usually only for 5 minutes. After that 5 minutes, he usually wants to join in on the fun and play with all the other kids. Now when he wakes up, he just wants to lay on the couch. When he does get off the couch, he cries or screams about everything. I usually end up putting him back to bed.

I also told them yesterday that they need to send him with better diapers as they should not leak after only having them on for an hr. Yesterday, I changed two pair of clothes because of pee!! Last week, he ended up gettign pee all over the playpen mattress. No sponging worked. I had to put it in the tub and squish all the pee out in the water. I had to lather it in soap and rinse many times. It took the whole weekend to dry and was barely dry on Monday. I put a mattress pad under the sheet, but it doesn't do any good if he rips the sheet off.

So this is what I have decided, since I have trouble talking to his parents about making changes:
-They are aware that he is tired all day here and doesn't want to take part in the activities.
-I have decided that if I plan an activity outdoors, he will come out too. If he is too tired, I will strap him in a stroller and recline the seat so that he can rest, or have him sit on a chair.
- My nap/eating times are going to be consistent, despite the schedule they have him on at home
- If he naps all morning because I have trouble waking him up, he still has to go back for a nap at 12:30pm with the others. If I have to give him a book or a quiet toy to play with for an hr to allow the others to fall asleep, I will. After that hour, I will remove the object.
- If all the other children are awake after my scheduled quiet time (2:30pm), we open the toy room door. I push his play pen to the wall (all while he is still sleeping) and allow them to go in and out as they please to get toys. To be nice (lol), I get them to play out in the living room. I keep the toy room door open though and he is exposed to all the noises in the house, including loud playing.
- I get him up 20 minutes ( at the latest) before his parents pick him up. If he does not wake up, I change his diaper while he is still sleeping, put his shoes on, gather his things and wait for mom or dad to take him out of the play pen. Sometimes, I will carry him out onto the couch if I do not have too many other children here.
- During the day, if he is exceptionally crank due to tiredness, I will put him down for a nap (if we are home). On a trip to the park, I strap him into the stroller while the other kids play. He doesn't get upset, so he must really be too tired to play.

I feel like most of his day is spent in the play pen right now. It makes me feel like a horrible person....like a bad provider. When I really think about it though, I realize that he is very tired, and needs a lot of rest/sleep. If I do not put him in the play pen, he is miserable. I also cannot change his schedule, as it would disrupt the others' schedule here.

Hopefully, this passes. I can't wait for him to be down to 1 nap a day.