How many times can your own mother screw your over before you cut her out of your life?

Let me start by saying that while growing up my Mom and I have had a love/hate relationship. I am now 33 years old and over the past several years my Mom had made several promises that she has failed to keep. First (and the biggest) is that she promised to help me out financially because I needed some dental work done. (after receiving a large sum of money after my Grandmother passed away). When it came time for her to write a check she informed me that she has decided to redo her kitchen and can no longer pay for my dental work. This was an unexpected $5000 my husband and I had to come up with on zero notice.
My Mom has also failed to keep several other promises and I have tried to cut her out of my life but my Dad (who I have a great relationship with) has begged me not to. Now I have a daughter, who my Mom adores, and a baby on the way. I am so afraid that she will start making promises to them and not keep them.
My Mom is a negative person and rarely has anything positive to say about anyone or anything. I could very easily cut my Mom out of my life and not look back but I feel like that I need to "put up" with her for the sake of my children.