I can understand your frustration completely. It is difficult to rely on someone or have expectations of being able to rely on someone when they are unable to live up to those expectations. It sounds like your turmoil may be revolving around two issues: expectation and comparison. You have expectations for your mother to do certain things or be a certain way and you are frustrated and maybe even jealous when you compare the time and attention your sister receives from your mother to the time and attention you receive from her.
First, regarding comparison, there are only two things that can come from comparison: pride and inferiority; both of which are unconstructive and self-directed. Both of those mindsets are hurtful to self and others, and both can lead to many other negative behaviors and emotions if not brought into check.
I am not saying that what you are feeling is anything but understandable. It makes perfect sense why you are hurt and disappointed. The problem is that it is eating you up inside! That part has to stop, and the only way you can do that is to release her from that expectation and stop comparing your relationship with your mother to your sister's relationship with her. It is the only way you can return to peace for yourself and your family and be the type of mother you want to be. If you keep being so preoccupied with this situation, ironically, your relationship with your own children could eventually begin to suffer in the same way that your relationship with your mother is.
The bottom line is that the only thing you can ever control is yourself. That includes what you allow to upset you. Again, I am not suggesting that it is illogical or irrational to feel hurt by how you feel your mother favors your sister, but what is fair? What are we really entitled to from other people? The more we expect, the more we open ourselves to disappointment. When we have no expectations of the other person, we diminish the control we give them to hurt and disappoint us.
Many people enter relationships with a 50/50 attitude. I am certainly not suggesting that there are not rules and boundaries and two-way/give-take standards for a relationship. What I am suggesting, though, is that if you keep your attitude (which is, again, the only thing you can control) as one who gives 100% and expects 0%, then you open opportunities for the other person to do the same and release them from reciprocating so that, when they do, it is more of a gift rather than a repayment to you. If you are constantly keeping track of what you do for them and how they return the favor, you will always only ever be tallying what you think she owes you, and she may not even know what those things are, especially if you have never discussed it.
I am not saying this to let her off the hook or put everything on you, but what I am saying is that, as counterintuitive as this seems, it is only way to restore peace to yourself by letting yourself off the hook, so to speak, of the hurt you feel when she does not meet the unspoken expectations you have for her. You need that peace, because I highly doubt that your mother is losing sleep over this as you are.
I know how it hurts to not be the favored child or to feel like a burden and an obligation to your parent, but the bottom line is that (and this will sound harsh and unfair, understandably) it really is not her responsibility to watch your children, she does not have to spend time with you or like it when she does, and, even if she were to lavish time and attention only your sister for the rest of her life, there is nothing that requires her to do the same for you. There just isn’t. You have to let her go. You have to so that she can choose on her own if she wants to be a part of your life on her terms. Then, if she chooses to be a part of it in any degree, and you choose to allow her to do so, it is all a gift because you didn’t expect anything, anyway, and you were looking at having nothing from her for the rest of her life. Something is better than nothing.
Release her from all obligation you feel she owes you. Figure out your childcare situation on your own, no matter what that may be, and remember that it is not her problem or responsibility to do so or contribute. Stand on your own and take what she does offer, whatever that may be, and you will be much more at peace and free to operate without the emotional upset that has been limiting you. I wish you the best, and please let me know if you are interested in any resources I can offer to you. Two great books for you to read are “Boundaries” by Cloud/Townsend, and “The Mom Factor” by the same author. They will help you gain the needed strength and insight to navigate this satiation with direction and purpose instead of reacting to what your other may or may not do. I really hope this helps you. I really am sorry that your relationship with your mother has been so hurtful to you, but perhaps you can establish a new relationship one day as a result of learning how to put your relationship in the proper context.