
Could well be kennel cough, particularly as pup has joined in :( KC doesn't necessarily present as coughing, despite the name. Quite often it is snuffles alone or a combination of coughing and sneezing.
Sorry, don't know the age of either your older dog or pup but as a precaution I think I'd have them checked by the vet. The youngest, most elderly and those with existing medical conditions are most at risk as secondary infections can set in.
In otherwise healthy dogs of say 1-7 years, it can often be treated merely with restricting exercise and, if symptoms are distressing them, with a children's cough tincture or honey to sooth the throat. They should be kept as calm and quiet as possible and, since highly contageous, avoid contact with other dogs for around 7-10 AFTER their own symptoms have lapsed.
HTH, Teri :)