The most important part is that YOUR energy needs to be calm. If you already say you're nervous thats not going to help. Your nervousness will EASILY spread to your dogs who then become nervous as well which might turn into aggression.
Meet somewhere neutral,be calm, and let them sniff each other. Usually if the Terrier is a little dominant towards other dogs the pup will feel his energy and very likely be submissive. It is important though that your mom is not pulling him back by his leash and that his leash is loose(if you want to have a leash on him), Tension on the leash will make him tense up as well.
So stay call and let them figure it out.
Dogs usually dont have a kill instinct towards other dogs.Even if the terrier tries to snap at him your pup will probably not fight back.It is very,very,very rare that theres a fight between an adut and a baby.
Disciplining on the other hand is something totally different. If the pup gets too rough with him or hurts him dont panic if the other dog snaps at him.Thats how dogs communicate and how a puppy learns.Usually though they dont have to use their mouth,they always use energy and body language first.