Hi, DeeJ, I'm sorry I don't have any experience with dogs not getting along, or adding a new dog to an existing pack, but I would think it would be more difficult with an older dog. You said Mary is 13 years old, so she is definitely a senior dog, and is used to being with the other two, and even with them you said she can be grouchy. Lulu is just a puppy, and probably has a lot of energy for Mary to handle. Mary is set in her ways, so it will more than likely she won't accept l
Lulu. You did everything right when you introduced them to each other on leash and by going for a walk, but being together off leash in the backyard didn't work out. I'm sorry they didn't get along. If you wanted to keep Lulu in your family, then you will have to keep them separated. My best friend has 3 dogs, they are Shitzu mixes, and her daughter has a Blue Heeler, these 4 dogs have always been together and get along really well. Her father has a family member to one of her Shitzu females, I'm not sure if its the brother, but he has been the only dog, and quite spoiled by her parents, he only ever really liked her father. My friend and her family moved in with her parents, (she's an only child) to take care of her parents, her mother has had Alzheimer's for a few years, and her father looked after her, but now he has Dementia, and has wandered a few times, and fell and broke his wrist, so they are now in a home, because my friend can't look after them by herself anymore, and she can't lift her dad to bathe him. She has all 5 dogs, as her daughter lives at home too, and her dads dog Usher is being attacked and picked on by my friends dog China. China has attacked him, and bit him, and made him bleed, she doesn't let him eat, he is an older dog, and that might be some of the problem, as the other dog seems to sense that he is weaker than the rest. It breaks my friends heart, as the house was Ushers and the only home he's ever been in, and now he's being pushed out and attacked. My friend feeds the dogs separately, and keeps Usher in the Master bedroom which used to be her Dads room, and she lets them out separately as well. The other dogs get along with Usher so they can be together, so she alternates them, and puts China in a separate room when Usher is out. Since the dogs are older its not likely that they will learn to get along, and so the only thing you can do is keep them apart if you want to keep them. Good luck, and I hope it works out, or you can find Lulu a good home if you can't keep them apart. Please keep us posted.