It sounds overwhelmingly like you need to become financially and otherwise independent of your mother. NOT punish her and cut her out of your or the children's lives. Just define what your roles are. It is not reasonable to expect to do that, when the way you're living makes those roles unclear, not only to the children but to you and your mother.
I hope I don't sound unsympathetic! These times are rough for most people, financially. Living with a parent can be a perfectly reasonable, sound choice, both financially and in terms of having a supportive partner in raising your kids and a second adult influence in their lives.
But you are saying that she is NOT a supportive partner and is instead undermining you. You have also described dynamics between you and your Mom that create conflict and chaos in the kids' lives. You compared that conflict to what went on with your exes. You also implied that the problems with your exes were so bad that you thank the heavens they are not involved in your kids' lives at all. You also say the conflict and confusion is making you depressed - which is not the ideal way to parent. So, the situation sounds pretty serious. Based on how you have described things, something must change.
The easiest thing to hope for is that if you dwell on how wrong your mother is - or get enough support from other people who think she's in the wrong - that she might be made to see the error of her ways and change. Then you could keep the parts of the arrangement that benefit you - the financial support, and not being completely alone with the kids - and lose the parts that are annoying and stressful.
But it's just not going to be that easy. If she's old enough to be the parent of someone nearing 40, her personality and ways of dealing with stress and responsibility will not fundamentally change. And she's in a legitimately confusing position. Even you describe her as more of a parent (albeit a second-tier parent) than a grandparent. And it sounds like she has taken on financial and other responsibilities for your children that seem more parental than grandparental. So it's natural for her to feel like a parent to your kids. But if she gets too close, or wants her own opinions about how to raise the kids to "count" as much as your opinions, then you feel like she's overstepping boundaries. Try to think about it from her perspective: You are OK with boundaries being crossed in some areas - like a grandparent helping support her grandchildren, instead of the parent supporting the children and just bringing them to visit the grandparent. But you want there to be clearly-defined boundaries, elsewhere. I think that situation would be confusing for most people, regarding something as emotionally-charged as helping to raise (and therefore getting attached to) children.
Let me offer an example that steps away from you and your Mom. You compare her to a step-parent, to explain how she should understand that she is #2 and you are #1. My husband and I are raising my sons from a previous relationship and his son from a previous marriage. All the kids live with us. Certainly, we have deeper bonds with our bio-kids, who have longer histories with us. (Which may not be entirely true, with your kids and your Mom. Has she been part of their lives since birth?) But, the way our blended family manages to be functional, happy and feel unified is that DH and I are largely equals, with all the kids. If I tell his son to do something and DH would have handled it differently, he doesn't overrule me - and vice-versa. Both of us help ALL the kids with their homework; volunteer at school for ALL of them; go out and do special things with ALL of them: cook, clean and care for ALL of them; and whatever money EITHER of us brings in is applied to whatever needs the kids have, regardless "whose money" it is and "whose kid" has a need. Therefore, we BOTH have some entitlement to be respected as parents and authority figures with ALL the kids and to have our opinions count, as far as how they're raised. I can't expect him to do all the work and contribute all the time and money as though he's a parent to my kids and then turn around and tell him, "Hey, these are MY kids. Back off. I call the shots, with them and you need to know your place."
But he's my husband. So I'm NOT trying to tell you your feelings about your Mom are wrong. I was a single Mom in my mid-twenties and cannot IMAGINE trying to raise my kids in a house with my mother. I love her, but I would have been miserable and depressed and she would have been very confused about who was really the parent and eventually the kids would have been confused about it. Yuck! What I'm trying to tell you is that the problem is not your Mom. The problem is the situation. If you're going to give her the responsibilities of a parent, she has some right to FEEL and ACT like a parent, instead of a grandparent. If you don't want that - which I can fully understand!!! - then you need to assume the responsibilities for your kids that she currently has.
I think many times, when we get depressed, it's because we feel stuck. Somewhere inside we know what we need to do - whether it's working harder at something we're slacking off at; or leaving a bad relationship; or moving on from something we're grieving over; or becoming more independent - but we're frightened of the change and don't feel confident that we can pull it off. And almost invariably, if we resolve to do what needs to be done and start taking the steps to make it happen, we feel empowered. Confidence grows. Depression shrinks.
Moving into your own place and handling your own finances doesn't mean you or your kids need to lose your mother as a close person in your lives. But it sounds like ALL of you need more definition about her role as grandmother and NOT co-parent. And it sounds like you are the ONLY person who can effect a change. I think you'll feel much better, on the other side of it, even though the transition will seem hard.