We have done Universal once with our kids (7 and 4 at the time) and Disney several times. We have not done both on one trip, though.
Here are a few thoughts for you, and you will get many other opinions

:
1. STRONGLY consider staying onsite at one of the Universal hotels for your time at Universal. Universal in general does not seem to handle lines as efficiently as Disney (my personal experience), and the Front of the Line access that you get with staying onsite is hugely valuable. Even if you stay one night at a Universal hotel, you get two days of FOTL access- check in day and check out day. With FOTL, you can do Universal Studios and IOA in two full days if you want.
Case in point: when we went to Universal last summer, Dr. Seuss's Trolley Train Ride had recently opened. There are two separate tracks, so of course we had to do both - many times each. The standby line was 30 minutes EACH time - we probably rode 30 times over two days. With FOTL, we waited about two minutes each time. We also were able to ride the other Seuss rides over and over again. There was not much that my four year old was interested in IOA, so riding the rides over and over in Seuss Landing was how she spent her time.
2. Which leads me to the next point - your 10 year old niece will have a lot more things to do and ride than your four year old DD, so I hope you will have two adults. DD4 was over 40 inches tall when we went, but she hated Spiderman and didn't want to ride anything remotely scary. We spent a lot of time at Seuss Landing, which is incredibly well-themed. Same was true when we went to Universal Studios - DD4 had no interest in Shrek, Jimmy Neutron, etc. She wanted to see the Barney show, and her 7 year old sister had ZERO interest in being seen at the Barney show

. We split up again, with DH taking DD7 and me taking DD4. DD4 did agree to ride ET, but that was about it past Barney. We spent the rest of the afternoon back at Seuss Landing while DH and DD7 did the rest of the Studios.
3. Now for the Disney part: My kids (now 8 and 4) have been to WDW five and three times, respectively. It usually takes us a full day to get out of Fantasyland in the Magic Kingdom, and typically DH will take DD8 off to do Space Mountain and Splash Mountain by himself. We always plan two full days at MK, and sometimes come back for a third day or at least an evening. If this is your first trip, you could easily spend 6 or 7 days if you wanted to see all four parks. Disney does their part by making a five day ticket only a few dollars more than a four day ticket - they want you to stay there longer. A four day adult ticket is about $215, a five day is $220. A two-day ticket is $140.
So my advice if you want to do both parks, whether you are staying onsite at Disney or not:
Come for a week or as long as you can. Spend one or two nights onsite at Universal. The hotels are beautiful and the perks are well worth the cost. You can get Universal done in two days if you choose. Spend the remaining four, five, six, whatever days at Disney. We always stay onsite - we love the transportation, the early entry, and the 24 hour magic. People are just as passionate about staying off-site - it generally costs less and there are much better options for larger families and groups. Plan to spend several days at the WDW parks - you will not run out of things to do!