I imagine this might be a question where you will get different answers depending on the norms and legal context of where you live. In particular, my impression is that the United States has much less support for taking time off and flexible work arrangements after having a child, than Australia (where I'm from) and many European countries.
For example, the standard approach in Australia would go something like this. The primary carer (usually the mother) would take maternity leave after the birth of a child. The duration varies a lot from parent to parent, but 4 to 12 months is quite common. When returning to work, it would also be common to come back to work on slightly reduced hours (e.g., perhaps 3 or 4 days per week; although full time is also common). Australia (and presumably many other countries) support this approach with various paid parental leave schemes and anti-discrimination legislation that requires employers to not discriminate based on parental status, birth of a child, and so forth. Such legislation and associated organisational policy (particularly in the university and government sectors) generally supports flexible work practices where possible.
The benefit of such approaches is that it makes it easier for primary carers to have some consolidated time with their children in the first year (and also makes breast feeding easier). Going back part-time also helps to shape a compromise between having a work life, earning money, and having quality time with your children.
Of course, there are many other considerations for families: financial, career progression, and personal interest considerations. Furthermore, the support of the university or post doc adviser in allowing for an initial period of time off and then potentially reduced hours is also an issue. In particular, because of the fixed-term nature of post docs and the nature of post doc funding, there may or may not be implications for the capacity to take leave or transition to something less than full time. And even where in principle it is allowed, post docs may be concerned that their CV will suffer or their supervisor may not feel that their contribution is as valued which may have implications for subsequent post doc positions.
More generally, it seems that universities, academics, and funding bodies and should take on the obligation of facilitating parents (and particularly mothers) in managing academic careers with parenting responsibilities. This is particularly important given the timing of post docs in people's lives. Not that this necessarily helps you, but I think that there are issues in Australia with this and the resulting reduction in the number of women who pursue an academic career, even with the legal and regulatory context. My casual impression is that it is much worse in the United States.
In terms of practical tips, it's tricky to make suggestions without coming across as trying to be prescriptive about what a good parent should do. But here goes:
If But perhaps, if you want more time with your children, enquire about taking time off after the birth of a child, and enquire about flexible work arrangements (e.g., 3 or 4 days per week). Would your post doc be extended based on time off and pro rata-ed for the days you work?