I potty trained in the daycare setting for years so I hope you will value my advice.
This first idea is something I only did with my own boys. Try just taking his bottoms OFF completely when you get home. He understands that he has to go to the potty to pee, so he should understand that poop does not go on the floor either. Just as insistant as HE is that he will not go on the potty: YOU insist that he is not allowed to put on a pull up OR underwear until he has done his business in the potty. If he is able to prevent himself from going at day care, he is definately able to "control" it.
I have 2 other suggestions for you in regard to pooping in the potty (this was copied and pasted from another post I responded to recently so please change the gender to boy):
1. Put a TV tray in the bathroom for her to have a surface to do activities in the bathroom. It can help her to relax if she is not just "thinking about it". Have coloring books and crayons handy (also, puzzles, books, etc. that can be done on the small table). This way she may sit longer too. Set a timer for about 15 or 20 minutes and tell her that when the timer goes off she can get up, but she can "play" there until then. Take the timer out of her sight so she is not compelled to look at it (if it doesn't beep when you push the buttons, you may want to add a couple of minutes when she isn't looking if she is sitting well).
2. Do you have a potty training doll?
I used to use it to show the kids how to poop. Get some tootsie rolls (without her knowing you have them or it will ruin it). Hold the doll over the toilet. Without your daughter realizing it, drop a few tootsie rolls into the toilet behind the doll. Get excited when you hear it drop into the water. Get her to look and see that the doll has gone poop.
It may or may not work, but it is definately worth a try.
I know this may sound "gross", but since kids learn by example you may even want to allow her to be in the room when you go (once or twice) maybe while she is in the bath (so she won't leave the room). Just a thought. I had my husband show our boys how to pee, but it may work for poop too. Shrug.
Good luck!
P. <><