Is completely normal - both mine totally different at daycare to at home (although DD was not particularly difficult). DS (3) no longer naps at home, but will at daycare - I said to him how do you go to sleep at daycare - he said "they get out my mat, I lie down, I shut my eyes and go to sleep - I said to him why don't you do that for me he said "because you are mum" :-).

Kids eat differently at daycare too, behave differently in other regards apart from sleep - it is pretty frustrating I agree. The way I make myself feel better about it is to tell myself that kids behave so well (including sleep) at daycare etc. when they feel safe and secure and happy at home - because they know they don't need to act up at daycare as can get the whole not sleeping fussing about what they eat misbehaving etc out of their system at home. :-)