My DD (June birthday) started school in September and whilst she is apparently impeccably behaved at school (according to her teacher), she is all the things you say at home. Some days she literally won't do a thing we ask her.
I am sure it is "just" tiredness. I think this was proved by her being a complete delight last week, when it was half-term, and now that she's back to school this week, she is back to bursting into tears, being difficult, and even wetting herself because she's too tired to remember to go to the loo (having never ever wet herself since she was potty trained!)
Cut back on all after-school activities. I mean all. We don't even do playdates at the moment as she is just too tired.
Just come straight home - a bit of TV, supper, bed as promptly as possible.
We are still being clear with DD about expectations (eg no being mean to her baby sister, she has to do what we ask her etc), but I guess we are treating her pretty gently, and not expecting very much from her after school. She loves her sticker reward chart, and we are trying to use that as a carrot and stick.
Every single other parent of a new Reception child is reporting similar behaviour at home, so I am consoling myself, and you, that it's normal and that this too shall pass!