Hi woody
Sorry to hear of your problem but this should be easy enough to sort out, they are fighting fo dominance both want to be the pack leader it is there instinct .
You or your wife will need to remove the problem by becoming leader and second in the pack if another human lives in the house they must become third or fourth and so on, the dogs must be at the bottom of the pecking order they will still want to sort themselves out but if you are recognized as pack leader you will soon be able to put a stop to that.
You say these are only ten week old puppies so they still only have there milk teeth ok sharp little pointy beggars but they nare not going to rip your hand off not untill they get a bit older anyway unless you get control of them now!.
Before anyone says it I am not suggesting cruelty in any way shape or form just don't be intimidated be firm with them when you feed them take there food back from them for a few seconds to begin with and gradually increase the length of time until they realize that you are the boss and you decide when and iff they eat that is what the pack leader does in the wild. You must control them or they will control you and instead of a pleasant dog owning experience you will be in for eight to twelve years of misery especially with patterdales they can be hard going the only other alternative is to get rid of one of them which seems a bit drastic.
Remember they are dogs not humans they can't be reasoned with only trained I have heard people say usually about badly behaved dogs it understands every word I say, no it doesn't what it understands is tone of voice, I bred and trained working gun dogs for over thirty five years and have handled hundreds but I have yet to meet one that speaks our language. Put them in there place and keep them in there place happy dogs happy people.
I hope this helps after reading it through it may read a bit harsh but in practice I can assure you that it is not and it works, forgot to mention if they need to be punished pick them up by the scruff of the neck and just a short jentle shake with a firm no is all that is needed just as there mother would never punish a dog when the moment has passed only at the time of the offense otherwise it won't understand what it has been punished for, use kind encouraging voice to praise them and sharp stern voice to tell them off and a small titbit at your discretion when praising them never goes Amis.
Regards
Berns
Ps sorry fo any mistakes used my wife's I pad for this seems to have a mind of its own I am not sure what it's doing most of the time