That is an awesome spider. I would not kill it (and its babies.)
I would carefully move it out of the house though. (To a garage or outhouse or shed...?) I actually did this some weeks back, when I found a pregnant spider in my kitchen. (Moved it into the garage...)
Several years ago, a pregnant spider got away from me, and crawled into a little hole in the skirting board in the hall, and for about 6 MONTHS, we had little spiders running around the hall and kitchen. (The hall leads on to the kitchen...)
Some days, we would wake up, and walk to the kitchen, and see anything from 5-15 spiders, and they all looked the same. They were definitely from that pregnant spider, and the same 'litter..' (Probably not the right word...) After about 6 months, they all seemed to disappear. It was June-ish by then, so they probably all went outside.
But yep, I would have to move it. As I said, I moved the one I saw the other week into the garage, so it wouldn't freeze to death! Now, I keep seeing lots of little spiders in there! The garage is 25-30 feet from my house though. (At the foot of my garden....)