If your company has a flexible hours policy, it shouldn't matter what exactly your reason for your taking advantage of the flexible hours policy. Whether your reasons are personal preference or external commitments, that's not their business. As long as your work hours doesn't interfere with you fulfilling your duties (e.g. you might have been more restricted if your role includes customer facing duties, or certain tasks that needs to be done at a specific times), your reasons shouldn't have mattered. If a parent on a similar role would have easily been granted to work at your proposed hours, so should you.
A parent with certain commitments to their child might have a stronger case than personal preference for the company to bend their policy for a specific employee with unconventional requirements, but these are out-of-policy arrangements that should really be considered in a case by case basis at discretion. A good flexible hours policy usually provides broad allowances for unconventional discretions, which is different from the nearly automatically approved flexibilities.
Personally, I would consider avoiding bad commute times as a perfectly normal, legitimate, and reasonable reason for taking advantage of flexible hours policy; especially if you shave 2 hours of commute times, if I were your manager I'd think you are a crazy masochist if you didn't take advantage of the policy. You're not a diva for wanting to save 2 hours of your day, you're just taking care of yourself, a happy employee is a good employee, a good employer would've wanted to keep their employees happy, as happy employees are more productive in the long term than ones who are stressed out.
<rant>Personally, I'm of the opinion that governments should have incentivised companies to encourage employees that otherwise would have had to travel through congested routes during peak hour to take flexible/alternative hours arrangements. This would've been a much easier and cheaper way to reduce/delay congestion issues that takes place during major constructions, as it would reduce the pressure to rush construction works and possibly even generate some revenue due to increased occupancy rates of transport infrastructure during non-peak hours. It'd also be a boon for late night business like restaurants.