from my understanding getting the extreme hardship waiver for the I-129f is extremely difficult, almost impossible unless you meet very specific requirements. almost always related to physical health (disability that prevents travel, extreme phobias of flying, tight spaces, home bound, etc.)
I believe the chances of you getting a waiver for this reason are extremely unlikely . Cause you technically could hire someone to watch your kids while you travel, or have other family watch them, or you have the ability to take them with you. I understand this would be hard on you and your kids to travel for that long, but it is not impossible. Key word being impossible.
your other option would be to go the spousal visa route.
this does still require an in person meeting, but only after getting married, which can be done online through Utah Online Marriage. the spousal visa has far more advantages than the K-1 visa. the foreign spouse will be a LPR upon arrival to the US and can work immediately. which isn't the case with the K-1 visa where they have apply for adjustment of status and work authorization. which is more costly and can take 6-12 months to receive.