I don't know what kind of hair you have, but here's my $.02.
The Duggar girls have perms. So, first and foremost, you should have at least reasonable naturally curly hair, or a good loose perm to achieve the curls they have.
Also, I think you are really missing an important step in how you dry your hair. The drying, in my experience, is what really makes the curls. My hair is naturally straight, and with mousse and a bowl diffuser blow dryer, I can actually get my hair quite curly.
**Wash and condition your hair, then comb or finger comb. Then, a good step is to apply a silicone based hair glossing product, like Citre Shine. It will ward off a lot of the frizziness that comes with naturally curly or permed hair. Once this is applied, go over your whole head, scrunching your hair with your hands to activate your curls to prepare it for blow drying.
**Next, apply your mousse/gel. You need to be sure you are using an adequate amount of product to completely coat your hair, all strands/curl sections, from root to tip. The fact that you say "no matter how much gel I put into it and when it dries my hair has a lot of dry strands of hair that end up giving me a lot of wispies flying around or frizzies flying around" tells me you are not using enough product. Read Riley J's response for the amount you probably need to use, to achieve a good, curly look. It's probably way more than you think. I have a cousin with thick, curly hair, and she'd use 5 or 6 handfuls (like softball size) mousse, and then use a spray gel on top of that.
**As for what products to use, I prefer Aussie mousse with leave-in conditioner in it... it gives you good curl, few fly aways, and leaves your hair really shiny from the conditioner. (My cousin with thick, curly hair likes this also, so it is good for different hair types.) Also, LA Looks has a good curling mousse, and some good spray gel for curls. You may need to distribute a lot of mousse throughout your hair, then add some spray gel as you dry each section.
**You need to dry your hair with a diffuser, preferably a *bowl-type diffuser.* You can scrunch your hair up with your fingers/hands, and place it in the bowl, and dry it section by section in the bowl. It will prevent a lot of those fly away's since you are not blasting air at the hair. You are basically *heating* it dry with very little air blowing on it. You take sections of your hair and place them in the bowl, and dry it section by section.
**Then, after getting the hair *mostly* dry with using the bowl diffuser, I'll just flip my head over and scrunch using my hand and the blow dryer with the diffuser still on. This just lets you get to the roots better, and do a little more shaping of the curls with your hand scrunching as you dry.
**Lastly, you need to use a good hairspray - Aussie Sprunch Spray is a good one for scrunching your hair some more after it's dry, and putting the final touches on scrunched hair.