I would just use the Train system.
But there are issues...
First off, will you have car seats if needed? Children 8 and under are required to have them in most vehicles, including Uber/Lyft,and they don't provide them.
As for a taxi, you are looking at over $100 each way for each trip (LEGOLAND is farther away).
So a train trip, to USH is fairly clear, take the OCTA Route 543 or 43 bus that goes up and down Harbor Blvd. (Note the American Spelling) to the Fullerton Train Station, Then take either the Metrolink or AMTRAK Train to Union Station, and transfer to the LA Metro Red Line Subway and take it University City. USH provides a free shuttle from the Subway Station to the park.You could also use the LA Metro 460 Bus from
Disneyland to the 7th Street Station and the LA Metro Red Line. Good thing, no need for Car Seats.
For LEGOLAND, you take the Metrolink or AMTRAK South to Oceanside, but then need to use a taxi/Uber/Lyft and Car Seats. They do make Booster seats that are inflatable if that is an issue.
I would also look at the Anaheim Tour Company or Starline Tours to provide transportation
https://anaheimtourcompany.com/