Hello.
I do not have kids but i do work two jobs, so take this for what it’s worth. My after-work training would sometimes get pushed aside because of a work related emergency etc. I would get so frustrated. So i started waking up before 5am to get my workouts in before starting work at 700am. Ill go to bed at 900pm so still getting in enough sleep but have less time in the evenings. I found a way to get it all in i guess.
But about sacrificing sleep, to me, sleeping, resting and eating is where your are growing/getting stronger from the stress load of training. So it may be as important or more than the training. If one is deficient in one of those areas, increasing training wont do anything. I feel guilty when im not following my training plan to the T. But i remember one of the coaches saying something to the effect of “i dont know what your plan is going to be in two weeks, because it is constantly being evaluated depending on your response to the training.” So regarding your sleep, i would suspect that if an athlete was monitoring their training response(ie: how tired your are, morning heart rate, timed workouts, or the like) and found that you were performing less than expected you would look to see if you are overtraining or not resting enough. Meaning whether you need more or less sleep will depend how you are absorbing the training. I think the goal kinda has to be, given my age, job, family, and other commitments, what is the maximum training effect i can have. I know, it sucks!