Will someone make a big deal of the fact we left minor kids in our home country till we figure out all the stuff (let's say 1-2 months)?
I doubt they’d worry too much, but your main problem would likely be all the Type D visas would have the same time limit on them so you’d have to get the kids over before the visas for them expire.
As your permits are already approved you shouldn’t really need to much more to get them issued. And is there some reason why you can’t get a bigger apartment to start with?
However, your time-scale is short, so I don't think you need to worry. I think that's the key thing to consider: whether you're sure, within your personal set of circumstances, that 1 or 2 months will not end up being extended and extended, until you're too late.
The conditions for family reunification are set out here:
https://www.fedlex.admin.ch/eli/cc/2007/758/de#art_44 (German)
https://www.fedlex.admin.ch/eli/cc/2007/758/en#art_44 (English)
You are well within the time limits set out here:
https://www.fedlex.admin.ch/eli/cc/2007/758/de#art_47 (German)
https://www.fedlex.admin.ch/eli/cc/2007/758/en#art_47 (English)
Please note that, in all official matters, any English text is a courtesy translation by the Swiss government, and not a legally binding text.
Welcome, soon, to Switzerland!
This is my personal experience: I entered first (non-EU), then my kid (from my home country) three months later, then my spouse, from yet another country, two month thereafter. We just kept everyone in the loop as to who, when, and from what embassy.