Puppies thrive on attention. Biting an ankle or a heel is bound to get a scream and a game of tag out of a child.
Wellies will prevent your children feeling the pain of a nip to the heel and so they'll be able to withstand it without making a fuss. By ending the game (of run around screaming while your puppy chases) all the fun is taken out of the biting this will decrease this behaviour dramatically.
When your puppy is jumping up, tell your kids to stand really still like a tree until your puppy stops. They should hold their hands flat against their sides and not look at your puppy. As soon as your puppy realises they are not getting attention for jumping up the behaviour will reduce.
3. Teach your puppy to sit
It is no good teaching your puppy not to jump up if you don't give him an alternative behaviour which will get him attention. Give your puppy lots of attention when he sits instead of jumping up. This will reinforce his behaviour and will get the jumping up to stop.
4. Give your puppy appropriate things to chew
Just like No.3, you need to teach your puppy alternatives. Teaching him what he is allowed to chew by giving him appropriate chew toys and redirecting him from chewing your things to chewing his chew toys.
Teach your puppy how to play by enticing him with ropes, balls, and other toys. Getting him interested in the toys is important so you need to be exciting with them. If your puppy learns that toys are what he's allowed to bite and rough around with, he will be less likely to play bite people.
All of the above points work in combination.
You need to ignore a behaviour you don't want and reinforce a behaviour you do want. e.g. stand still when your puppy is jumping up, and bend down to reward him by giving him cuddles when he is sitting down.
Remember: your children can not be the ones to teach your puppy to play appropriately or not to bite/jump up. Children can be hurt easily so make sure that you are there to ensure that your children are always safe with your puppy.