Your understanding of the sentences is essentially correct :) but I'll just provide a little more explanation to try and help and clarify the nuance.
ことだし is essentially an extension of the conjunctive 〜し, specifically the use of し for listing causes/reasons. (There's a post on all the usages of conjunctive 〜し here, if you aren't familiar with them: https://japanese.stackexchange.com/a/59151/33435)
The difference between 〜ことだし and 〜し is that the reasoning is be marked as more "objective" in the ことだし case. As a result, something with ことだし comes across a bit more logical, and stiff/rigid in tone. On the other hand, for the case of し without the ことだ, it is more relaxed as to the causal relationship being implied.
I think because the causal relationship is fairly clear, your translation of ことだし as "since" is good.
On your specific translation, I might consider changing how you translate 休み and 大掃除 depending on context and/or to sound more natural:
Tomorrow, since your father also has a day off, why don't we all go shopping?
Next week, since there is a guest coming, we have to do some spring cleaning/a major cleanup of the inside of the house.
Hope that helps!