The thing with them is, they are designed and bred to work and spend masses of time running with other dogs. If that natural instinct isn't fulfilled then they are going to find other ways of expending their energy. Which in your case is digging and jumping up.
He probably ought to have 2 or 3 good long (hr+) walks everyday, off lead so he can use his tracking instincts and brain. That way he will be physically and mentally tired. How about looking up some mental agilty things for him to do out in the garden so he has a distraction from just digging?
I've got 3 young dcs and I know how hard it is to fit in the dog's requirements around everything else that goes on in life. However, if you want him to be a good family pet without too many bad habits then he is going to need an awful lot of input from you.
I speak from semi-experience as my db has a beagle and it has utterly destroyed their house through boredom. As in, chewed through kitchen cupboards, ripped apart sofas, chewed their dining table and every chair, ripped up the carpets, scratched their wooden floors beyond repair, not to mention the £500 vet's bill after it ate a tube of tomato puree, metal tube and all!
They also get worse before they get better once they hit puberty.