Hi Gene, I'd like to help you with your question.
From your description, it sounds like you do your fair share of taking care of the kids. Coming home from your job and sharing in the care of the children is exactly how it should be. Your wife does work hard everyday caring for the kids. It is the hardest job in the world to be a parent. But you do an excellent job being there for your family.
That is not to say that your wife is not right too. Just in a different way. She does need to share in all the responsibilities in caring for the kids equally with you. At least as equal as you can make the situation, including getting up at night. But your wife is showing signs of burn out with her responsibilities. Caring for the children is constant, especially three kids all at such young ages. There is no lunch break, adult conversation, or even going to the bathroom by yourself. You cannot schedule your day in any way and everywhere you go, those kids go too so you have no freedom. Plus she is nursing, so not only is her attention in constant demand, her body is too. Mothers are a special lot dealing with that kind of stress.
My suggestion to you is to be as supportive as you can. Not only care for the kids half the time, but let her know how appreciative you are of the job she is doing. Bring her small gifts of appreciation. Let her get a bath by herself. Let her go out and get her hair done. Or even just take a nap.
Is there anyone who can stay with the kids for a short time? I know she can't do much outside the home because of the demands of nursing, but even a few hours helps. And it gives her time to focus on you without the kids needing attention.
Is there anyone to help her in the home? A part time babysitter, maid or other help during the day may make her job a lot easier. People have help in the work world, why shouldn't mothers at home.
Can you bring home dinner once a week? Pick up groceries for the family, even if it's just for the weekend?
I know this leaves a lot of the responsibility on you, and both parents with children as young as yours are under enormous stress. But once the kids are older (and it will happen much faster than you think!), your wife will have the time and energy to return the love and care you gave her at this time.
I hope this has helped you,