Hmm...I am on the fence. Granting every different type of flexibility isn't a legal requirement and, until it is, or until your new workplace has demonstrated otherwise, you have to assume they are old fashioned and the old rules still apply. It's completely foolish to do otherwise.
It would be nice (and make many more people able to work, not just mothers) if employers judged on output rather than hours in, and if there was flexibility over where and when hours are worked. However, not many organisations offer such genuine flexibility. You've said you have to do school pick up, they've said that's fine, we can offer you part-time hours. They're not paying you less because you're a woman, you're pregnant or you have a kid. They're paying you part-time because you will be part-time. If you want the full-time salary, work the hours in the way the business requires and arrange for someone else to do pick up. Needs must. (It's dreadful having to write that, as there is still a strong sexism argument that as most caring responsibilities fall to women, it's women who are usually forced into part time work and therefore take the hit to salary, promotion and advancement opportunities, and a decent pension...that's the motherhood penalty in action. No solution for that yet, despite laws that allegedly protect us.)
If you want a particular employer (one that supports mothers back to work, women at work, equal representation and pay etc), and you're lucky enough to be in a position to have the time to scour the planet to find one, then be open about your family and requirements. If you're at a point where you really need/want the job, don't mention you have a family at all. We like to think we've moved past this point, but we haven't.