I suggest that whatever form of discipline you're using it is not working. You're exhausted and perhaps the discipline is too difficult to maintain or perhaps it's just not a good fit with this child.
I suggest reading a book by Foster Cline and Jim Fay entitled Love and Logic for Toddlers or the one entitled Parenting with Love and Logic. They also have a web site you can find by googling love and logic. Their system is simple and easily applied once you get the hang of it. Discipline calls for consistent expectations that a child understands/follow and immediate natural consequences applied before the parent gets angry or "has had enough."
Does your mother complain because the 3 yo is out of control or because 3 kids are too much for her or something else. My daughter has 2 children 3 years apart. Both are high energy. Once the youngest was walking I could not take care of both of them at the same time for longer than a couple of hours. They are now 7 and 10 and it's just been this last year that I've taken both of them away from their own space at the same time. Might she complain less if you asked her to just keep one of them or even the baby and the 5 yo? Having one less child for you to tend to will help some. I suggest that the 3 yo is crying for help and perhaps staying with her mother for a few hours every week would help her feel more secure.
Another arrangement that helped my daughter and I was to arrange for babysitting in advance. And then to send an e-mail citing the date and time so that there would be no mix up.
Three and five year olds can play in their room for 30 minutes or so or perhaps longer if they are in separate rooms while you and your husband talk or just be together without constant interruption. It does sound like your 2 older children need more discipline so that they can learn to give you space. It could be that you're just too exhausted to make that happen. I understand that. But finding a way to get your kids back in your control needs to be top priority.
Other mothers, on this site, have suggested books. One that I remember is 1-2-3 Magic. I've skimmed thru that and it and I think it can be effective and may be an easier read than Love and Logic. They seem similar in their focus.
You could look for a mother's helper now that it's summer. Perhaps there is a young girl, 11 or 12 or older, in your neighborhood or church who would come to your house several hours a week to watch one or two of the kids while you nap with the baby or while you do the dishes or a bit of laundry or more importantly just sit down and do nothing. Mother's helpers have been discussed in several posts recently.
A teen may be available to do light housework for a small amount of money. If you go to church you may be able to find a retired adult or a SAHM with older children to help out once a week.
Do you have a friend who would be willing to babysit. I was single and had no kids when my friends were having there's. I loved baby's and kids and babysat for free.
If you don't have your older two sleep trained, then work on that. Get them to bed and if not asleep at least in their own room by 8 and you'll have time to be with and talk with your husband even tho you're still caring for your baby.
If you don't have a consistent routine, developing one and following it will help.
You didn't say whether or not your husband helps with the kids. If he doesn't perhaps you could encourage him to do so by starting him out with one task that he chooses. He must be sympathetic to your exhaustion and state of mind.
When you describe the way you have to treat your 3 yo, I suggest that much of your difficulty is caused by your exhaustion and inability to be sympathetic to her. She has been replaced as the baby of the family and she's feeling it. She doesn't know how to express her own anger and frustration. She has regressed which is normal. Feeding her is one way for her to not only get your attention but to also feel like a baby again.
She needs attention and if she's not getting positive attention she will act out. Negative attention is better than no attention. You've heard that. It's really difficult for you to give her positive attention because she isn't listening and is acting out. Someone needs to break that cycle.
If you can't do it, perhaps your husband can. Is he able to remain calm and maintain consistency for you and the children when he gets home or is he also worn out or not understanding of or able to be the anchor?
It's normal for kids to not listen. There are ways to improve their listening ability but I suspect that you're too tired to figure them out or to use them.
My mother had what we now know as postpartum depression. My father worked 2 jobs, one of which was 4 days on and 3 days off as a fire fighter. They struggled and struggled. They tried a part time house keeper but that still left us kids to care for and added managing the housekeeper. Church ladies brought us meals. A neighbor took care of the baby. Eventually, we 3 older kids went to live with an aunt and uncle and mother took the baby to live with another sister for 6 months. It was painful but was for the best in the long run. I'm not suggesting that you do this but telling you about it as a reminder to your husband about the seriousness of your sense that you're falling apart. You have to have a break, somehow.
I urge you and your husband to start counseling about how to manage your children so that you can get some rest. There are professional family and parenting counselors/coaches. I know of a couple who post on this site. I can't think of the titles they use. I've seen parenting coaches advertising in the freebie family magazines I see in stores and the library.
Yes, they do cost money but as you've said, you cannot continue as you are now. Because I don't know anything about your circumstances I can't suggest ways of getting money for this help but from reading your post I believe it's urgent that you find a way to get parenting help and babysitting help.
I also urge you to talk with your doctor about the possibility of taking some anti-anxiety and/or antidepressant medication for a while and see if that helps. Our body chemistry changes when we've been under stress for a period of time. You will benefit from some chemical assistance to get back on track.
