I think this is the best point about children and really everyone not aging in the game.
One of the most valuable features of Stardew Valley is that you can take your time, and if the amount you need is all the time in the world then that's the time the game allows you to take. There is no pressure other than the pressure you impose on yourself. The few things in game that run on a timer have zero consequences for you not finishing them. Help Wanted Board, Special Orders Board, Qi's Special Orders Board. Even the quests you've given can pile up for seasons and when you feel like finishing one, you can. Big things like the Community Center, Willy's Boat, and little things like the Largemouth Bass for Jodi or The Soldier's Star. If you don't finish any of these or you put them off 'til next year, then there's no penalty. Sure, you delay the reward but if you want to do other parts of the game your way, then you can. And visit those quests later. Muuuuuuchh laaaaterrr....
Time is a pressure that's most immediately felt on a daily basis, getting done today what you hoped or planned to do, but if you plan to take it easy and Fish or play in the Mines, or design your Farm all day/week/month, then have at it.
The rest of the Valley will wait and they will not ignore, judge, or age. They will be there for you when you need them.