Well I understand Millie's POV. She's old and hurting, and now a young pup is full of energy and around her constantly. To an elderly dog, this is like your wife opening up a day care center for 5-7 year olds when she's 92. That can lead people to become crotchety. I honestly do not expect Millie to change her behavior because she has always been the alpha in her pack. Her barking is likely a reminder that she is not to be challenged by the younger puppy, and that she's still around...but I would honestly have to see their interaction to identify the exact issue. I can only guess unfortunately.
Are you leaving food down? If so, that could be a problem. She will feel that she needs to protect her food by "standing guard" over it. If you only leave the food down for 20-30 minutes (long enough for them to eat) than Millie might lose the need to "guard" the food, and rejoin the family.