"Snape was right, you are helping him!" Hermione pointed an accusing finger at the two men, who were occupied with hugs. Although they were well aware of the childrens' presence as they did so.
Sirius was flabbergasted, not to mention exhausted, and it took all of his self-control not to grab Remus and smother him with kisses, but he was also a puppy on a mission. Peter Pettigrew had to be disposed of first, and then could come the reunion.