Welcome Millie! Have had a Border before-lovely character dog!
Re: jumping/nipping, needs to be on some form of a lead ALL the time, either a normal one, or training one-we now have them tethered all round the house (radiators, chair legs etc) so that you're always in control. When you go to stroke him, make him sit and slip your thumb/finger through his collar then when he goes to nip/mouth you, a gentle tug combined with a very stern NO BITiNG! Do this also if he goes for the DC and you have hold of the lead, give that a tug instead.
Tell the kids NOT to run if he chases them - stand still, fold arms and turn away shouting NO! We tried yelping if puppy did bite, but that just excited ours further!
Re:training to one part of the garden for toiletting, again, have him on the lead and take him to where you want him to go every time-this is taking us a while, as daft dog not picking that one up!
Not too bad a day here. Daft dog is calming down! Really! Am amazed but the advice above really works. She's still jumping up a bit when she first sees us as is excited, but isn't jumping at me so badly. Is jumping at DD though so need to train her to train dog IYSWIM! But the biting and nipping is much much better. DS regaining his confidence a bit.
Anyway, bedtime then walkies, love to all,x