Our flight arrives at MCO at 3pm. From there we need to pick up our car from Alamo, drive 40 minutes (says Google) to our house, stopping off at Target on the way for some quick essentials shopping.
Then we drive 30 minutes (says Google) to MK parking.
That takes us to, say, 6pm.
How long will it take to get from the car to Splash Mountain? We have tickets already.
We're due at Tomorrowland Terrace for the Fireworks Dessert Party at 7.45pm. I guess we can be a bit late for that. I'm (naively?) hoping, with a bit of FPP luck, to do the three mountains before we start dessert. Big Thunder and Splash are next to each other, and Space is next to the Tomorrowland Terrace.
You'll need one hour from parking your car to walking under the railroad station on Main Street. From there, add another 10 minutes to walk (with purpose) to Splash.
You won't be able to ride all 3 unless there are no lines. Your fast passes have to have at least 1 hour between each start time.
Space is not exactly next to the Tomorrowland Terrace. In fact, I'd factor in a 10 minute walk from Space to there. There's a long exit from the ride.
I would put the priority on the dessert party first. You've paid good money for it. Get as much out of it as you can. Ride some mountains after. The crowds should thin out after fireworks thus giving you a better chance to ride successively.
1 hour from parking to under the train tunnel is extremely conservative. On our trip last month it never took near that long. Once you park, there's usually a parking lot tram very quickly. Less than 10 minutes even if you just miss one. Then you have to go through security/bag check which can take some time, but if it's evening on a not high crowd level day it shouldn't take long. Then you have to do ferry or monorail. On one of our days, the express monorail was down and we had to take the resort one (ferry not an option with a monorail obsessed child). We still made it from beach club to inside the park in about 50 minutes.
A different day the express monorail was up, and the whole trip took about 35 minutes. Prepare for the worst, but you may be able to fit more in if you get lucky.
Wait times for the rides will be your bigger time constraint, especially if you can't swing rolling FPs.
30 min would be the absolute best case, 60 the worst case, and actual somewhere in between. There is no way you'll get all 3 mountains in 45 min. I would get a FPP for Splash at 7:00 (or there abouts), ride that, and then head to the party. Even with virtually*no* line, you have to allow about 15 min for SM because of the long queue going in and the long walk coming out.
Your drive times sound inflated. I've stopped at this Target (https://www.target.com/sl/hunters-creek/1790), which is 15 minutes from MCO and on the way to Disney World. Having stopped there in the past, I can usually be wherever on Disney property I'm going about an hour and a hour after my plane lands (say 2 hours, to be safe).
I looked back at notes from past trips and I did just that a few years ago and it took 45 minutes to get from the car to being in line for Splash. That seems to be a reasonable estimate for time from the car to the first attraction at that hour. You won't park close to the TTC, but probably won't have a long wait for bag check or the monorail/ferry.
Make your first FPP start time before you expect to arrive, maybe 5-6pm, since then you can make Big Thunder for 6-7 and Space for 7-8. You have a 15 minute grace period at the end of your FPP window, so you could arrive for Splash as late as 6:15 PM and be admitted with no problem (and, sometimes a kind CM will take pity on you if you're a little later and let you in the FPP anyway).
So, the bottom line is this is do-able. It's a little hectic, but sounds like a fun way to start your trip + if your flight is late an you miss an attraction, then adjust your plans, but if things go smoothly, then great! Also, sign up for Alamo Insider, so you can print your reservation from a kiosk rather than standing in line at the rental car desk. Unless there's no line, that'll save you a couple minutes at the airport.
One thing you haven't mentioned is collecting luggage and getting the car. You may have quite a wait for both, and neither is predictable. That could throw your timings, so just be prepared for not making that first fp.
Sorry, I missed the part about driving to the house first. You're going to be cutting in close, particularly if you plan to talk with your friend at their house. If you're just dropping off groceries with no need for chit-chat, then you might make it to Splash by around 6:15, but I'd probably push my first FPP back until 5:15-6:15 or drive straight to the parks from the airport (though, I'm not sure if that's an option for you).