Since you don't have EP passes or early entry, you need to make any non-HP headliner rides (Despicable Me, and the coasters) the first priority each morning or plan to do them single rider later on. Then move to the HP section after that. HP will be crowded, no matter when you arrive, since you can't do early entry HP, so be prepared for that.
You have two days, pick a different park each day to go to first to take advantage of low early morning crowds.
Arrive before official park opening. See link below for details.
How early to arrive at parks?
Ride any non HP must see rides first or save them for last or single rider.
IOA
The coaster here is Hulk.
Kong and Spider-Man are the other popular rides your adult children will probably be interested in.
Try to ride these rides very first thing.
Kong does not have a single rider line and as the newest ride is very popular right now. Head to it first if crowds will be high on your dates. Then, you can always use single rider for the other two rides if you need to.
US
Despicable Me - ride this first if it is a must see, lines get long early on.
Then head to the coasters and other popular rides.
Rip Ride Rocket and Mummy are the two coasters in this park.
Transformers is the other popular ride you guys may want to do.
MIB is also a fun shooting arcade game, similar to Buzz Lightyear.
All of these except DM have single rider if you need it.
After the headliners, move onto the HP section. At this point, the HP sections will be crowded. It's always crowded past early entry. Your best bet will be to use single rider for FJ and Gringotts. I'd save the other 2 rides (Hippogriff and Dueling Dragons) until late at night when the crowds will die down again somewhat.
If your dates are lower on the crowd calendar, you can try going straight to the HP section first thing when you arrive and you will have a little while before it starts to get crowded back there. In this case, you want to do the HP rides first thing. Then you can try for single rider on the non HP rides later in the day.
There isn't really any one way to tour HP that is best. Some people prefer doing the rides first. Some want to follow in HP footsteps. I think the main thing is just to take time to explore and see it all.
If you would like to follow in Harry's steps, here is a plan for that:
Harry Potter world as through Harry's eyes?
Here is a list of things to do in the HP sections. To really enjoy the HP sections, you need to take time to really explore and take in all the little details. If you only go and ride the two main rides, you may be disappointed, as I've seen people post after their trip that they didn't realize how much there was to do and see in the HP areas and were disappointed by finding out later there was more to see they missed out on.
There are stage shows, interactive wands, restaurants, the wand ceremony, and lots of little details hidden throughout the shops.
Does somebody have a list of all the "must do" HP things in each park?
For an explanation of the wands, see here:
Need info on wands for Harry Potter