Grumpy/ crying ( sorry, longer that i though it would be! )

[Bookworm]

Is mom giving him a morning nap? How long is the nap if so, and when does he get it? That may be a problem. Also, if he gets dropped off at 12:30, how long does he have to adjust to being there before nap time starts?
Mom needs to stop comforting him ASAP. This is not helping him at all. Do not go back in the room. Do not pick him up. You will have just undone all that you did before by letting him cry. Leave him there for the full time. He will quickly learn that at nap time, he is expected to sleep, and you will not come in to get him. Even if mom doesn't do this at home, he will learn that at your house he is to go to sleep on his own.
It sounds harsh, but if mom isn't going to help, then it needs to be this way, imo.

Also, the girl is probably just reacting to the unrest in the household. Try talking to her to see if she can tell you what is upsetting her.