If you didn't go further than the recruiter call, you don't really have a decision to make around that new job. I'd say, go through the interview process and see if they offer you the job. If they do, take that offer letter to your current workplace and ask for a matching salary and multiple days/week telecommuting privileges.
But really, I don't know your entire situation, obviously, but moving way out because there are better schools for your 18 month old's sake is not very smart.
If I may be so bold, I say:
Let go of the little details. Schools, etc. should not factor into where you live. "Tiny detail exaggeration syndrome" is a real thing. (MMM coined that)
Get the better paying job (increase your income during boom times as MMM puts it)
Move closer to the better paying job where you can walk or bike to work and, therefore, liberate resources (time spent during commuting, money spent on car, gas, etc.) and redirect those resources towards your happiness: Save the money, spend the extra time with the family.