It's a long way to go, and it might be something that the kids don't enjoy too much.
If you were flying into Miami I would say it's workable to land in Miami, drive to Key West, drive from Key West to Orlando a few days later then back to Miami to fly home, but the attractions for kids are fairly limited. Sure they have a great beach and nice pools at some of the hotels, but if that's all you're going to do that is available much nearer to Orlando with out a 8+hour drive.
It's certainly a workable trip for a couple of adults, perhaps if your dad has someone to go with it would be an ideal chance for them to take a 3/4 day break mid holiday to recharge their batteries , do something that is more adult orientated and do something they are interested in ( as opposed to focusing on the kids). IMHO the drive and lack of child friendly attractions (compared to Orlando) mean that the kids may feel it's valuable attraction time wasted on a side trip with nothing for them. There are few things worse than being trapped in a car for 8+ hours (TWICE) with discontented kids ( heck it's bad enough when you're taking them somewhere they actually want to go to LOL).
If you're looking at taking I27 for a lot of the way down there, whatever you do DO NOT drive at night/in darkness it's a difficult drive in the day due to the large amount of trucks that use I27 ( avoiding using the toll roads) night time makes that a dangerous drive. Using the Florida turnpike is a safer route , but neither of these would be "the coast road". To do that you'd have to take AIA which is very scenic, but it's a very slow route. The motorways are much quicker, but with the exception of the parts that take you over the Keys it's unlikely to be the romantic journey he's imagining.
IMHO it's one of those trips that seems great when you dream/think about it , but the reality is that it's never going to live up to the expectation. Certainly not with having kids along for the ride. I understand that when travelling with family it's nice to try and include a little "something special" for all those on the trip, but I think you're risking sacrificing a lot for the majority of the group to give one (or two) members something that will fall short of their expectations. If it's something he REALLY wants to do, I would try and encourage him to plan it as a side trip, without the whole group. Key West's best attractions are the nightlife and it would be much easier for him to be able to fully enjoy the area without having to worry if everything is "kid appropriate".
I don't want to put a complete damper on the idea, because I enjoyed my time there, but I don't think the plan, as I see it, is one that's going to meet with universal appreciation. JMHO.