I actually had a very similar experience my first trip to WDW. It was for 2 days, I had been to
Disneyland once, and had no plans to return to WDW in the near future. You can see from my signature that ended up not being the case!
Anyways - we had a BLAST those two days!! It's still one of my favorite trips
I'm not sure what time of year you will be going. We went in September and lines were very short, which allowed us to fit in quite a bit. But busier seasons also mean longer hours at the parks, so it might cancel each other out. I think if you plan on seeing just the highlights and aren't trying to fit in character M&Gs, you can have a great experience.
I agree with others that you need to have just a few must-do's in each park and focus on hitting the highlights and experiencing the overall ambiance of each park. A few specific tips from our trip would be:
1 - Epcot World Showcase is not very impressive when you are just rushing through it. If you can't allocate at least a few hours for walking around it, either choose a couple of your top countries and explore those or skip it all together.
2 - Contrary to popular opinion on here, we chose to only spend half a day at MK. We had recently been to Disneyland and there was a lot of overlap. It was more important to us to experience the new / different things in WDW rather than repeats of things we had already done. This is entirely a matter of personal preference, so you will have to choose what's best for you.
3 - If you will be getting in to Disneyworld the night before, you could try to watch Wishes from somewhere outside the parks (the dock at the TTC or from the Contemporary resort). This would allow you some additional park time on your days in the parks.
4 - Maximize FP+! You don't have time to wait in line for more than 15 - 20 minutes. However, you can hit most of the headliners if you smartly choose 3 FP+ and hit other headliners in the first or last two hours of operation each day. Make sure you have a good idea about which attractions will have the longest waits and schedule your days accordingly.
5 - HAVE FUN! Make sure to soak up the ambiance and enjoy every moment. Try to keep it from being about completing a checklist of to-do's, but rather enjoying each moment you are there. If something has too long of a line, skip it and don't look back. If you don't get it all in, don't be frustrated or have regret. Enjoy what you get to experience and make fun memories with your family.
I hope you have a really great time!