Maybe someone with a background in sociology can answer this, but looking at the trends we see that the paper is talking about a change of "happiness" of just one or two percent over 35 years. Is this really significant? Just looking at the trends, it seems the oscillations from year to year are much higher than that.
I'm not aware of any studies about happiness and its relation to freedom, so I don't know if that's true. My anecdotal impression is that caring for a child full-time is extremely difficult -- which is why the daycare industry exists.