I'll just say that you've skipped over the entire city of Los Angeles (the second-largest city in the U.S.) -- well, except for the part about flying in and out of LAX (LAX is in Los Angeles). Are you saying that you planned to transfer in and out of Los Angeles from Anaheim on the days that you weren't going to be visiting DL?
I'm assuming that you won't have a car. Is that right? If so, taking public transit in and out of the city of L.A. from Anaheim on alternating days is going to get tiring. Why not spend 3 nights in Anaheim and 3 or 4 nights in L.A. and then you can walk (in Anaheim) to DL and use public transit (in L.A.) to see the sights.
Here's a map of the various cities and the Grand Canyon that might be helpful:
Okay, let's look at the map:
1. The circles that are all piled up at the 9 o'clock position on the map are common tourist attractions in and around the CITY of Los Angeles. (The legend for the map -- which identifies each point -- is in the upper left corner of the page)
2. Point "F" (below and to the right of L.A.) is Disneyland in Anaheim
3. Point "G" (below and to the right of Disneyland) is San Diego.
4. Las Vegas is in the upper center of the map and Grand Canyon National Park is to its right (a 4-1/2 hour ride from Las Vegas). You can do 'day trips' to the GC from LV but that's 9 hours in a bus -- not recommended. So that means, 2 of your "Las Vegas" days will be spent exploring the GC and that's fine because 2 days in LV is plenty -- especially with children (who can't drink or gamble or go to many of the 'evening activities').
So, let's look at Los Angeles, Anaheim and San Diego. By train, it's a 45 minute train ride from L.A. to Anaheim and a 2 hour train ride from Anaheim to San Diego. This would suggest that it might make sense to use the train to transfer between the three cities so that you can stay put in L.A. for 3 or 4 days then transfer to Anaheim and stay put for 3 or 4 days and then transfer to San Diego. Of course, you can do this in either direction.
One option that might work for you would be to visit Los Angeles first (it's the closest to LAX), then fly to Las Vegas (and do your excursion to the GC) then fly from LV to San Diego, stay there for a few days, take the train to Anaheim (visit DL for 3 days) and then take the Disneyland Express bus to LAX for your return.
Our TOP QUESTIONS box at the right side of this page talks extensively about the CITY of Los Angeles and its immediate neighbors (Beverly Hills, Santa Monica, etc) including 'neighborhood overviews', 'itinerary ideas' and 'public transit tips'. The best way to plan your vacation is to select the attractions you want to visit and then decide how many days you'll spend in each area in order to see these attractions. You seem to be doing it the opposite way: deciding on the number of days to spend in each area and then finding things to do in those areas during those days.
Take a look at the TOP QUESTIONS and get a feel for Los Angeles and its neighbors and then check back with us with your more focused questions.