I don't doubt you but most people would not find a 2-hour one-way commute pleasant.
Anyway, a 2 hour commute is normal in the bay area . I used to do the south bay to San Francisco Caltrain daily... Flying is better. Free drinks for one thing
Different strokes for different folks.
For a 4 bedroom house, Zillow gives me around 7-8k a month in rent for SF and around 4k for SJ, so you'll at least break even and have a better quality of life for your family even if you won't see them much during the week.
Anyway: The fact that a simple adequate house for a family runs at 4k in the US is ... maddening. 1500 sqft is around 140 m², a comparable house in Berlin (one of Germany's hottest markets!) runs ~2500€. How one is supposed to live in the US when not on a typical techbro salary, I have no idea how y'all even manage that.