In my experience, your best bet is the use both comparison sites and carrier sites (Kayak, Orbitz, Cheapoair, etc. vs. Delta, Virgin, Southwest directly). I would also try to be flexible around your departure times and how many layovers you can tolerate with your kids. You might get lucky and score a good deal.
When you do search, I would absolutely make sure that you're browsing in Incognito/Private Mode. Travel websites check your history/cookies and will begin to inflate prices (ever so slightly) the more you search/the more websites you visit.
