In our experience, 1900 Park Fare can be notoriously slow. We have eaten there many times over the years because my DD has always been a big fan of Cinderella and the stepsisters. I think the shortest time it has ever taken us to have a meal there was about an hour and 20 minutes. We think it is a good day at Park Fare if we are seated within 10 or 15 minutes after the ADR time. It is not unusual to get seated quite a bit after your ADR time there. Hopefully, you will get seated around your ADR time. (I remember one time we had a 6:00 p.m. ADR, did not get seated until over an hour after that, and by the time we saw all the characters, left the restaurant at 9:00 p.m.- which blew my MK fireworks plan). Also, once you are seated, a lot depends on where the characters are as to how long it takes you to get out. The restaurant is big and the characters sometimes get really spread out. One time we had an ADR at 6:40. I can't remember when we were seated, but the last character in the rotation had just left our area when they seated us- by the time they all got around to us again (which was a must with DD), we left the restaurant at 9:20. That time I had planned for us to watch the MK fireworks from the GF boat dock, and we left the restaurant at 9:20 as the fireworks were ending.
I would be shocked if you could make a 6-7 FP with a 4:40 ADR at 1900 Park Fare, I think best case scenario, you are walking out of the restaurant around 6:00. I would book a throw away if you want to start one at 6:00- if you get really lucky and make it great, and if not no big deal.
Also, I think it is about a 15 or 20 minute drive from GF to Pop. I don't think Pop is that far from DHS- probably less than 10 minutes, but you still have to factor in probably at least a half hour to drive, unload the kids at POP, get to DHS and get parked and to the gate.
Would it be an option to put your Dad and Kids on the Monorail to MK to grab a bus to Pop on their own, or would that be too much for your Dad to handle? That might shave off a little time, and if you wanted to leave 1900 Park Fare while they were still waiting for the characters to finish their rotation you could do that. Of course, that might not be the best idea, because then the kids would probably be begging to go to MK.