It seems your mom has disappointed you. It's not your fault because she told you she would help and your expectations were high. The same thing happened when my son was born with my mother-in-law. She told me should would come to help me, blah, blah, blah. I was exhausted from a hard labor and my first child. Then when she arrived (she lived far away) she was obviously afraid of the baby. Not only was she no help, but she caused me more work. I felt similar to the way you and your husband are feeling now. BUT, that was a long time ago and I had years to work through it, so let me share what I learned.
My mother-in-law loved my children. She got great pleasure in them, and she wanted to be a help, but that was not the reality for what she could actually do. In those years I was near insulted as you sound to be now, but I must advise you to back off. Take what you can get and don't judge your Mom or have high expectations. No doubt she loves you and your daughter. Allow her to be the Grandmother she can be, and love her for it. Time passes quickly and my mother-in-law is gone. It took me many years to understand her, but I came to, and to love her deeply. I miss her and I miss that my children don't know her as adults.
All that said, if moving is best for your family you will have to do it......but do not do it to get back at your mom. Your in-laws may bring a whole new set of problems. You and your husband need to do what is best for your little family while considering and loving ALL the extended family. Try not to depend on others to solve your problems.
One more thing.....I'll have to disagree with the Mom's that think 16 months is too young to leave with a grandmother, aunt, or trusted babysitter. It's isn't your mom's comfort zone is all.
Hope this helps K..