Note that kW is a unit of power, kWh is a unit of energy

Your figures weaken the support for your argument (that staying at home is greener than driving to work) significantly: they suggest it's greener to drive to work as long as it's less than 90 miles away from your home.

I disagree with your calculation, but the point remains broadly the same. Here's an alternative calculation. According to Wikipedia, 1 US gallon of gasoline is equivalent to 33 kWh, so 100kWh is equivalent to 3 gallons US. At 45 mpg US you can go 135 miles, not 180.

You can look at this the other way round. Driving 60 miles at 45mpg US is equivalent to 44kWh of energy usage. For it to be worth staying at home for 10 hours, you would have be able to keep your home warm with less than 4.4 kW. That's roughly the power output of two old-fashioned electric bar heaters. Do you get freezing temperatures where you live?

It's difficult to be more precise because the figures depend on lots of things - how cold is the place you live, how efficient is your car, how you define "equivalence" between gasoline and other energy forms - but you've illustrated the following point very well: most people wrongly assume that the energy required to heat their home is negligible relative to the cost of driving anywhere.