Uffizi skip the line with kids?

I'm guessing the sort of thing you're looking for probably doesn't exist. If you want a guided tour, you'll pay each company's per-person price. The price can vary depending on length of the tour, size of group, any special features such as early entrance, and if they offer a discount for children.

For instance, Walks Of Italy charges $100.11 per adult for their nearly 3-hour, small-group (up to 15 people) early-entrance Uffizi+Palazzo Vecchio tour, $94.22 for children 2-14, and $96.57 for students.

Through Eternity charges € 59 (abt. $67.11) for their very small group (up to 8 people) 2-hour Uffizi masterpieces tour, €44 euro (abt. $50) for ages 5-17 and EU students, and free for 4 and under.

Dark Rome's price for a 1.5-hour, semi-private masterpieces tour (no more than 14 people) is running around $67.14 per adult, summer prices, and $61.45 for children 4-14.

I'm only referencing tours by companies which have had positive recommendations by forum posters.
Of the 3 I looked at, Though Eternity looks to be providing the deepest discount for children.

If it absolutely has to include a guided tour then I can't be of any help.
If you're willing to consider other options I suggest researching the "Amici degli Uffizi" card for your family. Can see the details on the Uffizi website, but basically it's an annual family membership that includes skip the line entry into the Uffizi, Pitti Palaca, Boboli Gardens, Bardini Gardens, and the National Archaeological Museum. We were in Florence earlier this month and the cards provided great value to us. They're about the only true "skip the line" passes that exist any more now that the Firenze cards require a reservation for timed entry. With the cards we were able to visit the museums several times each and enjoy them at our leisure - usually staying for just an hour or two before moving on.
Might add that the Archaeolgical Museum is really fabulous and might be of more interest to your kids than the Uffizi. Their exhibits of Etruscan, Greek, Roman and Egyptian artifacts is one of the best we've seen, with the added advantage of not being crowded.
Also for info, I just saw that the Uffizi is extending its hours on Tuesday evenings all summer - now open until 10 PM.

Info on the Amici degli Uffizi pass:
http://www.amicidegliuffizi.it/diventa_socio.php?pg=8&ln=en

But no, it doesn't cover guided tours of the Uffizi so you'd be paying additional for that on top of the membership.

Not that you intended to purchase them but feedback from some recent posters on making reservations if using Firenzecard seems to indicate that it isn't difficult (or wasn't for them, anyway) and EVERYONE must pass through the security checkpoint regardless of pass or ticket. The Firenzecard is also only worth the price if having time and inclination to visit enough of the attractions it covers.

This might be interesting for some of your children and is a free download:
https://www.uffizi.it/en/special-visits/monsters-at-the-uffizi

this is all so helpful thank you! I bit the bullet and bought two tickets to the Uffizi and now I wish I had done the family membership. at this point I may just get the Firenze card since I still need to get Accademia tickets and they are all sold out. Do you think with the card you can get in even without reservations?

I may just get the Firenze card since I still need to get Accademia
tickets and they are all sold out. Do you think with the card you can
get in even without reservations?

Reservations are now required if using the Firenzecard for the Uffizi and Accademia. So far I haven't heard of anyone not being able to get a spot by following instructions on the Firenzecard website but I'm also not holding my breath that will remain the case. Also, if you've already bought tickets to the Uffizi - an expensive museum - it really doesn't make sense to buy 85-euro Firenzecards just for the Accademia.

I just looked up the Amici Degli Uffici tickets. If I buy them online do we need to go get the actual tickets from the welcome desk? Because they are closed on the only day we can go. Or buying them online we are god to go.

Sorry, we bought our memberships (they're not tickets) at the Welcome Desk so I've no idea about picking them up elsewhere or having them sent. Maybe Robert knows?

You likely "looked up" the card on the site I'd linked above but if not, be sure not to use any other info on the net that might be very outdated. The Amici Degli Uffici annual membership, back when we bought it, used to cover many more museums than it does now so make sure this is the best choice for your situation? How many days will you be in Florence? If you only have 1 day to see the Uffizi, why wouldn't you book timed-entry tickets for that day for a much lower cost? Will you have time to visit the Pitti and Boboli/Bardini gardens with your membership?

Side note to Robert: You mentioned the Archeological Museum? I'm not seeing that one included in the “Gallerie degli Uffizi” museum cluster listed. Where am I missing it?

I agree with Kathy that if you're only there for one day then doing the timed entry is probably more cost effective for you.
If you'd still like to pursue it (and have enough lead time) then I believe they'll mail you the cards once you've completed the purchase on their website. Do confirm the details with them however - I'm going from memory here. To expedite things I suppose you could call them directly and handle everything over the phone. The lady at the desk speaks pretty good English.
As I recall there was a note on the Uffizi home page that alerted us to the fact that the cards were now accepted at the Archaeological Museum - a recent development apparently. The museum itself really is terrific - an unappreciated little gem in fact.

Thanks, Robert. I'll give a look on the Uffizi site, although I don't remember seeing the mention. Then again, I wasn't looking for it! :O)

Editing to add; here it is! I looked right over it, for pete's sake.

https://www.uffizi.it/en/pages/free-admission-to-the-national-archaeological-museum

What's very cool is that ANY ticket to the Uffizi gets you into this one, not just a Amici degli Uffizi membership. This museum also just happens to be on my fave piazza, and I've walked right by it. DOH! A treat for next time.