Your kitten is used to the company of other cats, but has never met a dog, and has met children only as visitors (on their best behaviour!). Please therefore take great care introducing your new kitten to any dogs and children in your home.
Children should be reminded that the new kitten is not a toy, but a living thing that can be hurt, just as they can be hurt themselves, and that the kitten feels pain when ill-treated just as they do. Ensure they know they should be gentle and quiet when handling him/her, and that if they are, the kitten will reward them by purring, cuddling and playing with them. Also warn them that a kitten does have claws and if they hurt or upset it, it may well use them to get away!
In most cases, the new kitten will happily begin to settle in with any resident cats and dogs from the start, but please keep a very close eye on the animals whenever they are together to start with to ensure no scraps break out, and for the first couple of weeks at least, do not leave the kitten alone with older animals when you are out of the house or at night – always place him/her into a separate room to ensure that nothing untoward happens when you are not there to deal with it. This practice can be discontinued once you are sure that the animals have all settled down together.