I'm sorry you are having this difficulty.

Yes, depression can certainly cause a person to feel fatigued. Plus, if you're on psych med's, they can cause you to feel groggy & fatigued as well. I don't take anything anymore. But back when I did, I was typically only on a single antidepressant. Yet I always felt sort-of groggy & out of touch, so to speak. Plus I think when a person has the sort of difficulties with family members you describe, that can also add to one's depression, anxiety & lethargy.
Here are links to 4 articles, from PC's archives, that talk about how to handle the overwhelming fatigue of depression & find motivation. Perhaps some of the ideas in these articles can be of help:
5 Tips for Dealing with the Overwhelming Fatigue of Depression
5 More Tips for Dealing with the Overwhelming Fatigue of Depression
Tips for Finding Motivation When You're Depressed
12-Steps to Creating Motivation When Depressed | Relationships in Balance