You kiddos are pretty close to my kiddos ages, within about a year of each kid.
That said I think if you can get a reservation within the first 30-45 minutes of dinner dining reservations, it should be ok. The reason why I say this is because the signatures can take anywhere from 1 1/2 to 2 1/2 hours, closer to the 2+ hour mark for just adults. So, if you show up at 6pm, you may not leave until 8pm or later. And as you go further past the opening mark and your waiter has more patrons, the slower and longer it will take for your kids to get their meal.
I can tell you that my hubby and I went to Flying Fish this past November for our 10th Anniversary and we were lucky enough that my just older sister took my 2 kids, then 7 and 5, to Beaches and Cream while hubby and I had dinner. Our ressies started at 6:15pm, no kids. We finished at near 8:45pm, or maybe closer to 9pm. My sis just called us as she was taking the kids around the boardwalk to see were we were at for dinner so she could plan more - we were in early stages of dessert and stuffed, so we left after she called within 10 minutes or so.
I think if we had had a ressie b4 6pm, especially closer to 5pm, we could have made it within 90-120 minutes. Honestly though, I can't see getting out of a signature in under 90 minutes and that's pushing it...jmho...
If you think your kids are ready for that, then you're set to go.
Our kids were boarder line even 8 months ago. But, we took them to a Simply Fondue place last month and that meal took around 2 hours. They got bored after about 90 minutes, but the dessert fondue brought them back to life, lol. At the time, DD was 8 yrs to the day and DS was 5 3/4 yrs.
If this is a "romantic" dinner for you and hubby, honestly, I would book them into one of the Disney Club night care places for the 2-3 hours. Your kids are both old enough for it and almost all the signature rests have the clubs near them. They are exceptional for kids and my kids have tried them 3x so far and complained every single time we picked them up!! (once, we only took them downstairs to the Wilderness Lodge Cub's Den and DH and I ordered room service upstairs and had a night in, and they were still mad that we picked them up only 2 hours later, lol) Plus, they include dinner for your kids. We "softened" the experience each time with our kids by bringing home leftovers, esp 1/2 or more of the desserts, lol, and they loved it!
Where are you thinking of going?? My kids are now begging to go to Flying Fish this next trip,

, and we may take them there, but we may have them try out the Beach Club night childcare to try out Narcosse our trip in Dec.