I spent ten days in Orlando this July... Yes, I realize this was a poor life choice, but it had to be done. There was a convention and I had to go, so free trip to Orlando for me! Doing Universal cheaply is totally possible - and it puts the classic time-money tradeoff to work. I am a teacher on a budget, and this was a splurge trip for which there was nearly no budget.
I took advantage of my free plane tickets and went a day early and stayed two days longer than I needed to be there, plus I had a friend in town who was happy to join me for evenings in the parks.
For Universal, I'd get Power Passes for everyone and plan on 2 trips for each pass by planning the next just before the pass expires. That knocks all of your park tickets for two trips down to $90 per person - no matter how many days you go, and everyone can make their own decisions about it each day if you want. I went ahead and got the preferred pass because it had no blackout dates and was STILL cheaper than four days in the parks over two visits, plus I got parking and discounts for food and suchnot. If one of you got one of those, that would save $$$ on your food as well, and you might even find the savings enough to justify an on-site hotel like Cabana. With an unlimited-use pass, you do not have to decide which two days you'll go flat-out through the parks. You can decide to go this morning or that afternoon, and relax other times, breaking up the times you're in the park and allowing people some chances to make some decisions.
I stayed at three different hotels for the various parts of my trip. For the Universal part at the end, I stayed at the Country Inn, about a mile and change down the road from the Citywalk, and it was about $60 for the night and included a continental breakfast. There's a shuttle that goes a few times in the morning and a few in the evening, or you can take what's called the I-Drive Trolley, a little-spoken-of transport mode sponsored by the I-Drive chamber of commerce or something, and run by the MEARS mafia. You pay $14 per person for the week and ride as often as you want. It'll actually drop you off fairly close to the entrance of Citywalk, which is the only way to get to Universal. There's some hoofing it, but it's manageable. Littles may have an issue unless you have a stroller. Also, a cab or Uber ride to/from the hotel is cheaper than renting a car and paying for parking each day.
Food on Citywalk is nothing like the Disney situation. You have all sorts of normal, average, run-of-the-mill type places like Panda Express and some Yogurt place that escapes me at the moment and Cowfish Sushi, which I'd consider to be at the upper end of the dining options on Citywalk. You can eat in the parks and it's a little bit more expensive, but I didn't find it to be gougey like Disney's prices. Also: Citywalk food is absolutely nothing to write home about, while I still have dreams of my Le Cellier steak of 2013 and am counting down the days until I can have Baklava in Morocco again. Seriously. Disney food is amazing. You don't go to Universal for the food - you go for the rides, and the fact that it's way less marketed to the littles because so many of the rides have height requirements. You can also score gift cards for the restaurants on Citywalk on Restaurant.com and various other redemption sites. This could be a great way to get some of your meals covered.
And for your transport from the airport? Consider the local public transit, known as Lynx. It goes to International Drive, and connects into the trolley system that can get you to your hotel. I got from the Airport to my hotel near Sea World (Red Roof Inn, then Doubletree by Sea World) in about 40 minutes in a one-seat ride for $2. The bus driver was super-friendly and so were the locals on the bus. Pack your patience, because they only leave every half-hour, but they're cheap. When I told the 300 delegates of the Washington Education Association that they could ditch their $22 shuttle for a $2 one-seat ride to the airport in about the same time, it brought down the house and everyone was clamoring for more information on it.
Frugal is fine, and if Free Dining gets your family the vacation they want with the budget you want, then I get that. Disney relies on that ease to keep capturing your dollars, and Universal is doing its best to be different, which means that it works differently. You WILL end up spending more time trying to save money at Universal, but if your family wants a slightly different vacation, and some variety to it, consider that there are other ways to do it outside the Disney bubble.
Good luck!!