Ok, this is a tough situation.
First, I would say that if overall you have had a good relationship with your day care provider that you work with her to find a solution. You are the only one who knows your history with her, go with your gut. I would NOT assume that she is lying to you for her own convenience. Generally folks don't get into the day care business because they want a "convenient" work life. = )
Unless you have other trust issues with your provider, see if you can work with her to a) get answers to your quesions and b) figure out something that works for your son. The questions you've written up above seem to be the first things you need answers to - and it is not a bad idea to know exactly when other people/staff are in the house with the kids anyways. I would recommend that you set up a time to talk with her to discuss your son (talk about his general progress as well), preferably at a time when she is unoccupied. My daycare provider has some time to talk each day when the kids are all down for their naps, or set up a time to call her in the evening or on a weekend. The best way to have this discussion is all at once and when you're not rushing to get out the door (and when other parents aren't coming and going as well.)
From what you say, it does seem that your son might be needing that little pick-me-up nap in the afternoon, perhaps he can be put down for it a little later, say 4/4:15. Then when you pick him up, he'll be fresh and hopefully in a fun mood. My little ones are both into lots of sleep - the oldest is 4 and still takes a nap most afternoons at home, but only once in a while at preschool. It wasn't unusual for her to sleep for up to 4 hours for her naps - often we had/have to wake her at 5pm so that she would be tired enough to go back to bed at 8pm! My new little one (6 months) takes a little nap in the late afternoon also for about 1/2 to 1 hour. I pick her up at 5:20 every day. She's in a sunny mood with that little nap, so I'm glad she gets it!
However, from what you're saying, your son is getting the same amount of sleep with one nap at daycare that he is getting with two naps at home on the weekend. He is also old enough to *want* to stay awake, especially if there are other kids there to interact with - older kids are fascinating to younger ones. It's very possible that he is excited enough when the other kids come over that he doesn't want to go upstairs and lay down.
You may need to consider that he is naturally moving on his own to one nap - although it is longer, so he's still getting the same amount of sleep - and rather than trying to push his bedtime later, you may need to move it earlier, if you truly think he is cranky from lack of sleep and he still is not taking an afternoon nap. Try putting him to bed at 7pm and seeing how that works.
Unfortunately, he can't be forced to go to sleep, so if he won't take that second nap, then that is the way of it.
I understand about wanting more mommy and daddy time - I work full time too and my youngest goes to bed at 6:15/6:30 - that means I have less than an hour with her each night. Same thing happened with my older child when she was this age. It sucks, but it is what she needs, so we do it. I spend more time with her in the morning than in the evenings most weekdays and I try to make that fun time (and I love having weekends with her.)
Good luck!