> although she still goes mad when we pick him up
Is there really any need to pick him up? I know it's easy with smaller dogs and puppies but it's better to train and encourage a puppy to come when called, go to bed etc without resorting to picking him up and putting him there :)
Many people recommend waiting for at least two years before adding another pup to the household - it's great to have an older one nicely trained and sensible before adding a hooligan and of course it means that they are better spaced out in old age. However now he's there it'll be worth reading about how you can raise puppies together as your younger one is still very much a baby and you'll find they soon learn to play together and ignore you!
Give them a bit of space using baby gates, when needed, and train them separately and you'll find that things will settle down a bit in a few weeks. Give it time - my pup was 12 weeks before my older dogs started to relax and interact with him