The "trick" to entering a park is to look at ALL the lines. For example, at the security check point, make sure you and your family have all bags off your body and all compartments opened up. Then, scan the lines and try not to get behind a group of people who haven't done the same thing. This includes families with strollers and bags under the strollers that they don't realize need to be put on the table and opened up. That takes the time you are waling up to the lines. You could be behind someone who is slower but it's no big deal. BTW - your entire family doesn't have to go one behind the other. Both sides of the security tables will be open so you can split a few on each side.
At the ticket turnstiles, same thing. Look at ALL the lines and if there is a green arrow on the stile, you can enter. Frequently, there will be groups that once one person goes in a line, the rest of the group follows. And not just groups traveling together but groups that have just emerged from one bag check line and just follow the person in front of them. Here, however, I would advise to keep your family together and enter the line in a row. That way, if one of you has a problem, the others will know about it. This takes maybe a minute or so.
Also, you can put your bags back together after you go through the ticket turnstiles or reassemble while in line for the second queue. Or, you can go off to the side and do all that and then get into the ticket turnstile lines.