I lasted 6 months (gave notice at 4 months 8 weeks notice was required contractually) at a large law firm. It SHOULD have been a dream job. Money was insane, large office, it came with a promotion from associate to senior associate, opportunity to seek specialist accreditation, conference and travel budget, networking opportunities fairly early in my career etc... etc... blah blah blah. It was awful from day one. The culture was like a shark pool, everyone was out for themselves and deliberately undermined and back stabbed.
The pressure was intense to achieve billable hours (which were 7.5 per supposed 7.75 day). Like you ,I had a young son - whom in the interview process they had assured me would be just fine as they were such a family friendly firm pfft!
For me no it did not get better. For me I should have left sooner. I don't regret leaving it taught me that that culture is not for me. If that means I work in smaller firms for less money than so be it.