UCLA seems no better and no worse than other large research universities in terms of treatment of women. Visit your department and talk to people before you take the position.
Having a child while a post-doc at UCLA was in some ways wonderful and in other ways terrible. On the plus side were massive amounts of flexibility and top-notch onsite daycare. On the minus, those massive amounts of flexibility have a career cost, especially if you're on a short-term appointment.
Also, be careful when reading HR policies. Plenty of them do not apply to post-docs. I had a child during my second year of post-doc, but during my first year I had been paid entirely via a grant. My title and employment status changed after the first year. I had not been in my *new* position for 1 year at the time I took leave, so UCLA said that I was not eligible for FMLA. We worked out another arrangement so that in the end I did take 6 weeks or so, but there was no official policy supporting that.
Job Satisfaction Level
The career track to a tenured position at a research university is long, uncertain, and especially challenging for women given the way it lines up with typical family-starting years. UCLA doesn't seem to be worse than other large research universities in this regard, but it's not any better. When I had a child during my post-doc, it was treated as "surprising" or "brave" by many of my colleagues.