It is not workable for all three of you to commute every day. That is pure madness. Is there any way you can buy a bigger place somewhere close to work? Then your inlaw, and most importantly, your young child, can stay with you in your own house. I am sure your MIL is wonderful, but your child is so young. Wouldn't you love it if you can watch him/her grow up with you?
Short Hills, NJ is a good school district. Many Chinese families live in Bergen County, NJ, so I suppose the school district can't be that bad. Or if you are willing to get outside of NJ, how about Westchester, NY, or Long Island? There are many good school distrcts in those places. Or if you don't want to live too far away from Manhattan, how about Queens? A single family house will cost you somewhere around $700k, but the commute may be more manageable, and your family can be together.