Not sure if that will help you but my grandmother was one of the most important person in my life, I had a very strong bond with her how ever in many ways I think her relationship with me was a bit unhealthy. We lived with her for a while when I was little (in her house) when we moved out again because my mom had found a nice flat, she would tell me that she missed me so much she cried and wandered around the house calling my name because she had forgotten I wasn't there anymore. She was a very emotionally manipulative woman in many ways, I didn't see it as a child and my devotion to her was absolute, sometimes above the one I had for my own mother. As an adult I understand why she acted this way, she was a terribly unhappy and insecure woman who had been hurt many times over by her loved ones in her life (from childhood). Now of course that doesn't excuse what she was doing to secure those she loved in her life but it explains why she was doing it.
One more point, very important one I think, is that despite her manipulations there's was so much more to my grandmother than this and she genuinely was a kind and loving grandmother who would have done everything for me, she never once let me down in any way and I knew I could always rely on her. The fact that your mother in law is perhaps inappropriately emotive towards your dd in someways concerns me a little less than her false promises and her letting her down. Emotional manipulation often masks a deeper hurt and insecurity which I think deserve sympathy not suspicion. You should however do what you can so that your daughter knows that granny is exaggerating how much she misses her so your daughter doesn't feel burden by this.
This is how I view this based on my experience, taking into account the empty promises along with the over emotional stuff, I'm not sure if the situations are similar or not. I guess only you can tell if your mil is being manipulative for hurtful selfish reasons or because she is feeling insecure in her relationship with did or her son or even with you and is desperate to offer the world and then can't deliver.
Having said all this (sorry so incredibly long) in either cases I think you need to protect your dd from feeling hurt by mil letting her down and from the burden of your mil happiness/sadness because neither of these should be her concerns or responsibility. I don't know if the best way is to discuss with dh and/or mil or to go directly to dd and lower expectations a little. Ie. Granny said she might be able to come over today, but we're not sure yet. Or, of course granny misses you when your not there, just like you miss her but she is a grown up and she doesn't really cry she was just exaggeration so you know how much she loves you.
Hth