Likely, yes. I don't know what this woman's issue is, but narcissists do this. They loooovve babies, but once the child reaches the age of 2-6 years they lose interest or become abusive. It's because babies are fully dependent on their caretaker and they feed the narcissist's need to be adored and be the center of attention. Once they get a little older though, the child starts to express their own will and wants and may become defiant. Because, as normal people understand, children are unique individuals with their own personalities, ideas, and desires. But to a narcissist, the child only exists to fulfill the narcissist's needs, not to have any of their own. The child is seen as an extension and reflection of them, and any perceived flaw or failing of the child is a personal affront to the narcissist.
My own mother told me many times throughout my childhood and into adulthood, "You were just the sweetest baby but when you turned two, man, you became a real *****." I don't think anyone in their right mind would describe a two year old that way, especially not a mother talking about her own child, but my mother always thought that statement reflected poorly on me and failed to see how it reflected on her. My guess? I was a normal two year old who started to express my own will, and since I was no longer a perfectly compliant human baby doll, she started to resent my existence.
I would guess the Turpin woman is similar. Love them when they're adoring, attention-garnering babies, (figuratively) dispose of them when they no longer fulfill that role. (Which reminds me something I wanted to ask those of you who saw the Turpin Facebook page: Were there any pictures of her while she was pregnant? I was unnerved by the dailymail article linked upthread where the neighbor said she never saw the mother pregnant, but several new babies showed up in the time they lived there. Add to that a 49 year old woman with a two year old, and I'm just wondering if we're going to find out these people are baby snatchers.)