Earlier quoted context omitted.
In this scenario, is there a way to handle the promotions such that no one is upset? I can't think of one. Maybe put them on different tracks -- those who took "parental flexibility" can get promoted, but it occurs later, and the money saved from that deferred promotion gets given to the singles who put in extra time/effort? Not sure, just brainstorming.
Now you're in what is probably textbook discrimination territory.
But how far do you take this? Is not getting a promotion penalization if your coworkers are more likely to be able to participate in work that garners praise?