Does this sentence make any sense: After 4 days of being sick with my wife being out of town and two kids, my house has reached maximum entropy.
Yes. Definitely!
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It is readily intelligible but "with my wife being out of town and two kids" does not read very well: "with" does not distribute easily across the two phrases. This is one way to try to improve it:
With two kids, and with my wife out of town, after four days of being sick my house has reached maximum entropy.
It is good style to write small numbers in words.