What's more relevant is where the child's Moon is in relation to their Pluto. Moon in a birth chart describes, very loosely, how the native sees their own mother, what kind of mother she is to them. If the native's Moon is in aspect to their own Pluto, that's when there's an especially Plutonian quality to their relationship with their mother.
A Pluto/Moon conjunction in synastry can speak to an intense relationship, but it depends on what else, if anything, is involved in that aspect. If the mother's Pluto is also conjunct the child's Moon, then we've got that intensity. If the mother has any personal planets in conjunction, square, or opposition to her child's Moon (and her own Pluto), we've got that intensity. If it's just mother's Moon conjunct child's Pluto, we only have one testimony to the intensity, which means it probably won't be as super intense as you expect.
More relevant is the fact that the child was born while the mother was having a Pluto transit to her Moon. That says something about the quality of her experience of becoming a mother to this child. If it's her first child, then we're looking at a Plutonian quality to her experience of becoming a mother in the first place. Maybe there was something Plutonian about the pregnancy and/or the birth.
Could be. Possibly, becoming a mother brought those feelings up for her.
It's also possible that there was some shakeup in her family, her relationship to her own parents, or her home situation. Having a baby is in itself a shakeup to the home situation, so that alone could have been it, but there are other possibilities.
The theme could also show up in something to do with whichever of her natal houses has its cusp in Cancer, and/or whichever house she has her Moon in.
My daughter was born with the moon conjunct my Pluto. She is my first born and the experience was extremely intense. From the moment my labor began, it was intense. There was a point where she almost died, and they had to stop my labor. In the end I ended up with an emergency C-section and I almost died on the table because of an overdose of anesthesia. My Pluto sits at 29° Virgo and my daughter is 7° Libra. Some consider that a wide aspect, but I can tell you my experience was extremely Plutonian. She changed my life in so many ways and our relationship is beautiful and yes very intense.