To actually be helpful:
1) Keep checking with Delta - people cancel/upgrade/move seats. Trying to get three seats together will be tough, but you may be able to get two .
2) Try to get at least one aisle seat - they'll be easier to "trade" (see point #5)
3) Get to the airport early and ask again when you check in. Upgrades/cancellations may have come through since you checked in and/or people moved around when they checked in and a pair may now be open.
4) Ask again at the gate. Again, upgrades may have cleared since check-in and/or no shows (which wouldn't have been known when you checked in) may have opened up a pair of seats.
5) Ask the people sitting beside your single seats if they'd be willing to trade. If you managed to snag aisle, you'd be asking people to move from a middle seat to an aisle seat, which, unless they are traveling with the person in the window seat (I'm assuming a 3x3 config), they are likely to be willing to do. Do not just sit in the seat and then ask the person - ask as if you know they'd be doing you a favour.
ETA - don't count on them automatically fixing it for young kids. Kids from the age of 5 can fly alone, so the airlines certainly think that they can sit alone. There was a story a few days ago of a mom who ended up separated from their 2 year old daughter - there is only so much the airline can do, once seats are assigned. Also, the computer (which assigned the seats) has no idea how old anyone is (unless you have a, rare, child fare), so it doesn't prioritize which groups it keeps together and which it splits (actually, it probably does, but based on passenger status and/or fare class - things it knows).