What symptoms would you see if someone was in the third stage of dementia?
If a dementia patient is forgetting that they have just had a meal and not recognizing family members and asking to go home to their crying baby. would you say this is third stage dementia?
The behaviors you describe are typical of Alzheimer's starting in mid-stage but much more prevalent in the later stages of the disease. People at this stage lose sense of time and space and also lose their ability to gauge their appetite, consequently there will be times when they refuse to eat and others when they'll claim to be famished shortly after having finished a meal.
Likewise not recognizing a relative and "wanting to go home" are very common in the advanced stages of the disease. Communication is particularly crucial in these situations. At all cost you'll want to refrain from arguing or contradicting them. It simply doesn't work. You'll only manage to bring stress to both of you. Instead, validate and work with her perceptions while putting her mind at ease.
Example on handling the food issue: Your mom says, "When is lunch? I'm hungry. You're starving me!" She finished lunch 10 minutes ago, but instead of trying to get her to accept that (which she won't,) you simply say, "We'll be eating in a little while. Can you hang in there? Maybe you could help me with this . . ." (and then give her a project as a diversion.)
You can use similar approaches with the other issues. When she gets anxious to get home to her crying baby, it's important that you understand that she has entered an altered reality and her anxiety is real. You can help her by offering her a solution by saying, "I just called your neighbor. She's happy to care for your baby. She's such a good friend, isn't she? - - - Could you give me a hand with this . . . ?" (give her a diversion)
As you can see there's a simple routine to follow: Acknowledgement, solution, diversion.
Forgetting names and particular relationships is part of typical Alzheimer's memory loss. Even knowing this, it's often hard for us not to take it personally. The simplest solution is for the relative to introduce herself in an informal tone, i.e. "Hi Gramma, I'm Susan, your grand-daughter. I'm so glad to see you. My mom, your daughter Valerie, sends her love to you."