I suppose the real question is whether you can weather the storm long enough for the market to recover. And beyond that, how cynical you are overall about everything taking completely before that can happen. I wonder a lot about that second one.
3 years is really not a long time. So I'd say it comes down to emotional fortitude and probability of staying employed. If your time horizon is longer than 3 years, the calculation of whether to sell should essentially come down to calculating your odds of keeping your job. I bet it's possible to build a robust mathematical model that recommends a decision given your best personal estimate of your layoff probability during a severe market crash.
My personal time frame is 4-5 years of emergency funds. You can adjust that for your own risk tolerance, but have a look at various past crashes to make an educated decision.
I'd only leave it invested if you don't actually need it, because college can be delayed or financed with student loans.