When you have children, why should evolution be seen as under pressure to make you happy? If the ultimate goal is to ensure that you will care for them for the time necessary for the offspring's wellbeing, there are various ways to do this without making the parents happy; in fact, making the parents happy may be counterproductive.
Well, the parents are not happy all the time. But when the offspring are safe and happy, the parents will be generally happy. Should a threat to the offspring exist, the parents will not be happy. Seems to fit with the gene's plan.
I think it BCZ actually doesn't stem from happiness or even lack of it (say hello to functioning unhappy parents). Children give strong "purpose" and hijack the dopamine circuitry which is the real driver behind human drive, evolutionary speaking (yes they also hijack some other circuitry as well, but the real drive is the dopamine system). TLDR, you're right, it works on another dimension which is even more fundamental than happiness dimension. The dopamine circuitry stems from lizard brain and quite old, evolutionary speaking.
Just a note, the Triune brain theory, implied by you saying "lizard brain", is not actually part of scientific consensus. It was incredibly popular (even being cited by Carl Sagan) and still retains a lot of popularity among the public, but it seems it is no longer regarded as factual.
> "The preponderance of the cerebral cortex (which, with its supporting structures, makes up approximately 80 percent of the brain's total volume) is actually a recent development in the course of evolution. The cortex contains the physical structures responsible for most of what we call ''brainwork": cognition, mental imagery, the highly sophisticated processing of visual information, and the ability to produce and understand language. But underneath this layer reside many other specialized structures that are essential for movement, consciousness, sexuality, the action of our five senses, and more—all equally valuable to human existence. Indeed, in strictly biological terms, these structures can claim priority over the cerebral cortex. In the growth of the individual embryo, as well as in evolutionary history, the brain develops roughly from the base of the skull up and outward. The human brain actually has its beginnings, in the four-week-old embryo, as a simple series of bulges at one end of the neural tube."
Despite what that paper says, the lizard analogy goes to this, and I agree it's loose, outdated and misleading one but doesn't change the argument we're discussing here.