I've heard this is an old wives tale. In fact, my midwife and OB caution against listening to it. Often women think their babies should quiet down and that is often the first clue of fetal distress. I'm sure different baby's activities levels drop off or pick up, but if there is a major slow down of movement, don't assume that is suppose to happen. They told me my baby shouldn't slow down in the least and if he does call them immediately.
I'm a FTM, so I can't speak from experience, but this is what I've been told as well--"cautioned against" is the perfect use of words. Even while in active labor, you should feel the baby moving. Don't let your MIL throw you off -- maybe you'll have your baby soon!