I left Facebook/Instagram earlier this year. MPK is very family-friendly, I'm sure you and your family will enjoy it.
I lived in Palo Alto in a 2BR/2BA apartment near El Camino and California. Not the most luxurious space, but it did me just fine. I was alone, so I Airbnb'd the 2nd room, earning about $2k a month. My rent was $2700, plus ~$100 for utilities and Internet. I made enough that the $2700 wasn't a big deal if I had to eat the whole thing, but I was alone, so I optimized. MPK's free food definitely helped me keep costs low too, but of course, that doesn't quite help the rest of your family.
These are questions best answered by Peeps @ FB, but you're not the first, and I'm sure they have plenty of resources to help you out.
All said and done, it's definitely doable, but depending on your salary, it could be tight. If you want a bigger/cheaper place, consider MV, Cupertino, or Redwood City, or even San Jose. Heck, Oakland's a great option too. Check the shuttle schedules to see what works.
I enjoyed my time there, I'm sure you will too. But ultimately, you have to answer this for yourself!