dilldill, i was looking tonight in a book which miriam stoppard was involved with, and this sort of behaviour is entirely "normal" in a child the age your daughter is...they don't all do it but it is normal if they do.
involving strategies are good, rather than instructions - "let's do this" rather than "you do this" or "i bet you can't" rather than "if you don't mummy will be cross" etc.
when you have a strong minded child they do need more "encouragement" to be good than a more biddable one - there's no point thinking "she should do it anyway" if she won't - a small reward when she does, even if it's only a big hug, will be more effective than a punishment when she doesn't.
she will grow out of it, but you want to still be on good terms when she does. we all have days when we feel we're doing everything wrong and all the problems are our fault, but we aren't, and they're not.
so "what story shall we read in bed?" will work better than "go to bed now". or - to quote penelope leach - "i bet you can't tidy up your toys before i've peeled these potatoes" is better than "clear this mess up now!" (and you also have to remember, with a child who speaks and understands well, that they are only nearly 3 and don't really grasp as much as you think - my elder daughter was just 3 when her sister was born and i shudder to think how i over-estimated her comprehension because she spoke well...)