Yes, there is a separate number, but I don't have it handy. Call the WDW-DINE number and ask them for the number for Group Dining. They'll give you the number and transfer you if you ask.
Just so you know...with 10 you can use regular DINE line. Groups is usually 13+. For the group, you will be offered very limited times....usually the first 20 minutes or last 20 minutes of the meal times. So if the restaurant you want serves from 5-10, they take PS from 5 to 9:40, so you will have your choice of times between 5-5:20 OR 9:20-9:40. They will not promise to accomodate groups any other times.
However, we couldn't eat that early or that late a couple times with our group of 20, so we made two PS for groups of 10 through the DINE line...you have to use different names and phone numbers as one person cannot technically hold 2 PS at the same restaurant for the same meal. When we arrived at the podium, we let them know we were together and could we please be seated together if at all possible....and we were willing to wait extra if they thought they could accomodate us. NOTE: They do not have to try to help you do this!! But they were able to seat us together both times...
If you can eat early (since you've got all those kids with you) I'd just do that as they can have the table ready for you and should be able to seat you without a wait if you're one of the first PS of the night. Less trouble for all involved if it will work for you...
Good luck!