Starting a story with a pronoun is mysterious, I'll admit, but unnecessary when you reveal it's a house not six words later. How about,"The house was dull - duller than dull. It seemed..."
Looking at the phrase, "monotonous way of living," it sounds like you couldn't think of a better way to describe it. How about,
"The house seemed to mock life, suck it out of its inhabitants, and spit it back as tedious, uneventful, monotony."
What does it mean to "take life slowly, unchanging and unfeeling."? I'm not sure that's a clear description.
I wonder if needless comparisons are necessary, like "stiller than a rock on the moon," or "rivaling a child's top." I prefer a stripped down approach. I should add that abverbs, in most cases, aren't your friend. Lastly, with what grip is the house holding them there. You haven't established that. I don't even know if I'm supposed to take it literally or figuratively. How about,
"The and house and those inside were still like a rock while the outside world spun around at a dizzying pace."
I don't need to point out that "rained, rained, and rained" is repetitive. How about,
"especially on those days when it seemed to rain forever."
What does grey house mean? Lots of houses are grey. It's either an unnecessary detail or an unsuccessful attempt at portraying the house as a depressing place to live.
You haven't exactly said why the house is a terrible place to live, just that it is.
We all know that sheets are neither cold, nor hard (especially after you've been laying in them). So this line isn't effective at evoking anything.