unaccompanied woman with children to enter KSA

I suggest you delay your arrival .

If you will arrive on Work Visa - you can not leave the Kingdom until you get iqama and then exit-reentry visa.
If your wife and children have own visas they are free to travel alone. But usually they can get residence (or visit) visa only after you get iqama (or your employer has big wasta).

Wife and kids have their own visas. But, my employer told me kids enter the country under my visa. We may delay the day of arrival.  Apparently, there's no easy solution for this.
Thanks

If you need to return to the US three days after arriving here, why not just come after the surgery?

Once you arrive here, you cannot leave till you get your residence and labor cards, and that can take anywhere from a week to 3 months, but typical 6-8 weeks.  And usually dependents arrive once the bread-winner has his/her residence card.  I have heard of exceedingly few cases where the whole family has come together to SA.  Nearly always, the man comes first, then the family follows a couple to a few months after.

Your wife and your children are classified as your dependents.

Trapezius wrote:

If you need to return to the US three days after arriving here, why not just come after the surgery?

Once you arrive here, you cannot leave till you get your residence and labor cards, and that can take anywhere from a week to 3 months, but typical 6-8 weeks.  And usually dependents arrive once the bread-winner has his/her residence card.  I have heard of exceedingly few cases where the whole family has come together to SA.  Nearly always, the man comes first, then the family follows a couple to a few months after.

Your wife and your children are classified as your dependents.

The twist now is that he said "wife and kids" have their own visas....

If they have their own visas then they are free to travel...you just come here after the surgery ... that's all.

Unless, your wife is Saudi and you are the "legal guardian" please clarify your statuses to get a clear answer from us.

An American, I've lived in Jeddah for 25 years.  During this time, I have taken the kids home for a vacation without my (Arab) husband at least 15 times -- maybe more.  I did this when they were infants, little kids, and teenagers.  I was never asked for any kind of proof that their Egyptian father approved of this, whether he was with us or not.  The issue did not come up.

My husband had arranged the "exit and re-entry" visas, though.  Maybe his signature was enough?

If a woman is entering Saudi with kids there should be no problem as long as the passports and visas are in order.  Usually, the airline staff will check to make sure that these documents are available before the plane to Saudi takes off. 

If you are worried about this, check with the Saudi consulate before you go.

On the other hand, if a woman is leaving Saudi with her kids, the airport officials may require proof that the father approves.  It's best if he's there to see them off.