After receiving the second NOA how long is itr afterwards for the embassy to get it? We have children and I would like her to be here for their birthdays.What more could they ask her to show we have a real marriage. We have children Does that help to speed the process up knowing that we have children?

hey, look at you with a timeline and everything!

I don't think I've seen a K visa from Belize, so I don't know how speedy they are, but I would suspect that it's "pretty fast" after NOA2. It's never fast enough.
After approval at the Service Center, your file is sent to the NVC, which is a part of the Dept of State. They will look briefly at an I-129f and send it on to the Consulate. Check with other K-3 people to see how long it stays at NVC.
Once it gets sent to the Consulate (and there may be a delay at NVC while they wait for "enough" paperwork that needs sending to BZ), the consulate contacts your wife with "packet 3". She and you can start getting those documents ready now... police checks etc. If she does not know where to get these things, the instructions are in "packet 3". If she is close to the city, she can always try asking at the consulate if they will give her her packet ahead of time.
The rest of the forms can be downloaded from the internet.

Then you wait for the consulate to tell you it's time for the interview. This will depend on their schedule, and unfortunately, you don't have other people's cases to check out for comparison. I would not get antsy about it happening quickly though. Be prepared for another couple/few months.