Have you been to one of the US Disney parks? How old are your kids? When you say Italy, what city or cities are you specifically referring to?
So: without knowing any of the above...
I am going to assume you are from the US, have been to either CA or FL, that your kids are neither babies nor teens, and that you are referring to Rome and/or Venice, have never been to Europe.
1. Lodging. Don't stay out at Disney, unless you want to stay in a Disney hotel for the experience. It's super easy to get on the train in central Paris and do a day trip to Disney. It would be a major pain to stay out at Disney and day trip to Paris. Because...
2. Paris the city deserves the lion share of the time. Usually I can entertain myself for three days in parks in California...and a week in FL. I was done with both parks in Paris after a day. It's beautiful but TINY and other than walk throughs, and a few unique attractions, it doesn't have much- in fact it has a lot less than both Magic Kingsom or DL. It has less shopping, less food, fewer rides. No splash mountain, or jungle cruise. If I'd had young children with me, I could have probably spent 2 days. Maybe. And that would include significant pool/nap time. As it was, most of the time in the park was spent in line for tower of Terror as CA is getting rid of it. Everything else was practically walk on, but a lot of the rides are closer to "kiddy" carnival rides than what you might expect at a Disney park.
In contrast, I had a week in Paris and probably would have filled up another. If not in the city, then with Day trips. And I think your kids will love Paris- it feels like a "theme park" with the river and the monuments and even the transportation. The Metro stops are all different (definitely take them the art metier stop and museum). The metro signs look like something out of Jules Verne. The gargoyles at Notre Dame should thrill them if they've seen the hunchback movie.
3. I'm reluctant to say "no" to Italy, because that might be where your interests lie. And Venice would be fascinating/magical to kids. But I think London is the easiest city to get around, and it has tons of kid friendly attractions. Basically, though, I'd do Paris/Venice or Paris/London. You DON'T have time for all three, and Rome would be better left for a time when the kids are a bit older and you can spend a whole week just there. Its transit sucks. Crowds are immense. It has a lot of history and art that I'm not entirely sure young kids would appreciate. I actually loved Rome but it's a lot of work to sightsee there. And I'm an enthusiastic walker and did not have to drag a stroller or kids stuff around.
So anyway..3 nights for Venice and 6 nights for Paris. Or 4 nights Paris and 5 nights London. Or use all 9 nights in France- you totally could, it might be the most relaxing option, and there's definitely enough stuff reachable by train to keep you occupied for twice that. Train stations tend to be in the center of towns while airports tend to be out in the middle of nowhere. Any flying days will take up more time than train days. Eurostar (train to London) takes up more time because remember, you have to go through passport control to enter the U.K, so the process is a lot like flying.
It might sound like I didn't enjoy DLP, but I did. It's probably the most whimsical of the parks- the details are stunning. But I think people who have been to the US parks before might feel a little let down, especially if they are there for the rides or shopping rather than the atmosphere. As for tickets- the Disney website had the best deals that I could find. I'm sure it was just a winter special, but I got a park hopper for half price. So check there first!
