I can't tell for sure, but from your comment that there are two later flights ATL-SYR, I'm assuming that you are on DL 1412 MCO-ATL 850a-1020a, then DL 1258 ATL-SYR 1100a-109p, or something close to that. I wasn't sure of your dates, but the current schedule is showing 40 minutes - they may have adjusted it by the date of your flight (and they may again).

In any case, 35-40 minutes is just barely a legal connection in ATL, but you may be OK. It looks like your MCO-ATL flight is regularly scheduled to arrive into gate B1, and the ATL-SYR flight is regularly scheduled to go out of B21. While this can change between now and then (and may change that day based on daily operations), if those gates hold and you are reasonably on time into ATL, you should be able to get from B1 to B21 in time, even with kids - just be ready to move.

If you are indeed too late, DL will generally protect you, but don't assume. If there's a long line, go ahead and get in line but call DL on your cell to see if the phone agent can do it quicker. Be ready for the fact that reticketing could break up any family group seating - there's really nothing you or DL can do if the only remaining seats are scattered.