I agree with the part I highlighted. However, if your family REALLY wants to do all 3 parks in 2.5 days during summer, it can be done but you will need to go open to close or be willing to miss some things. You will definitely want (honestly need) Express Pass for the theme parks. Crowds this spring break have been crazy and will be this summer as well.
Stay in one of the premier hotels because EP is included for the 2 theme parks and you can walk quickly to the parks. I would choose Hard Rock for such a short trip because it is SO close to the theme park entrances. Portofino is our favorite, but you will not be spending time at the resort, so go for the closest hotel. Staying at HR will ensure you do not waste even 1 minute on boat rides to/from the theme parks.
For 2.5 days in 3 parks I would do:
Day 1 - Start at VB and bring a bag with dry clothes for a theme park after. Be in line at VB an hour before Early Entry. (We were on the first bus from our hotel last Labor Day weekend and were the 3rd family in line). Go to the right when you get in, dump your stuff on some of the free chairs and go straight to Krakatau (water coaster), which is on the right behind the volcano. We rode it twice back to back and it only took about 30 mins. Then move on to the big drop slides in the volcano. From there, pre-plan what other slides you want to prioritize and plan to leave VB around 4:00-5:00 (change into your dry clothes at VB). From VB, I would take the bus to City Walk and eat dinner at a City Walk quick service and then go straight to one of the parks. (If you want more of a break, you could make a ressie at a sit down city walk restaurant - but I would not waste my time). If you go straight from VB to City Walk, you can dump your water park bag at one of the big pay lockers at the front of the parks. Do a few rides quickly with your EP and jump in line for Hagrids or Velocicoaster right before close.
Day 2 - Do early entry at IOA and hit Hagrids or Velocicoaster (the one you didn't do the night before). Finish up IOA and take Hogwarts Express to Universal Studios. Do Gringotts and Diagon Alley. Then make your way through the rest of that park.
Day 3 - Start at the park where you may have missed something or pick your favs to re-ride.
The key to ensuring you maximize your time is to do a theme park after VB. Your family will want to study the maps for all 3 parks and choose your must dos so you can prioritize them. Then once you are there, Universal really requires no planning at all. This may sound like a lot of planning, but it really isn't. I just went into a lot of detail since you are new. Keep asking questions because the experts here are really helpful.
ETA: many people utilize the Annual Pass hotel discount strategy (upgrade one ticket to the cheapest AP so you get the hotel AP rates). However, those AP hotel rates are getting hard to find. I upgraded to AP last fall and it was worth it because I had an AP rate for that trip. Unfortunately, I wasn't able to find an AP rate for my upcoming May trip and others are reporting similar experiences here. So book an AP rate if you can find one and then upgrade one of your tix after you get there (you don't have to show your AP until you check out). If you don't see an AP rate, snag the Savvy Traveler rate if you see it.