Before we make the long drive, how can I check to make sure they have not reach capacity limit?

Use the Disneyland mobile app.

Website or app.

Leave home early, arrive at opening?

I've found that the late winter and early spring are good for smaller attendance. All holidays are crowded.

Download the disneyland app. Not only can you see park informations, you can also check the current wait time for most of the rides. Of course, arrving early (before park open) will always guarantee admission.

Also mid to late August is great, especially on weekdays. Once area schools are back in session, attendance at the park drops by like half.