I have a key for my Mum's (need one - she's housebound). I knock when I arrive, but I just walk in once I've knocked. Hubby knocks and walks in at his mum's (I knock and wait for her to open the door). Our daughter still lives at home, so it's not an issue, but once she does move out I would expect her to knock, then come in. Our next-door neighbour's children used to knock and walk in - it was far easier than answering the door to the three of them coming and going all the time (our daughter did the same at their house too - basically, between the 2 houses we had 4 children - a casual observer would have struggled to work out which actually belonged where, even early in the morning when they were all in their pjs!!).
Whilst I agree that your children need a key for your house in case of emergenies, they should not be just walking in if you don't want them to. Sit them down and explain that, as welcome as they are in your home, it is YOUR home and you expect them to treat it as such - and wait to be invited in.