I have access to a place with small feral hog population and a green light to take whatever I need. Right now there are 3 adults as far as I can tell. 1 Dominant female with 8 weeners, 1 male slightly younger, and 1 pregnant female who looks like she will give birth fairly soon.

My plan is to take out the "leadership" with archery in a manner that doesn't scare the other ones away and maintain a regular supply. I'm sure at some point they will catch on and move away, but for now the idea is to get them to stick around for as long as possible.

The dominant female is less afraid, the male is vigilant and keeps a watchful eye, and the pregnant female runs away whenever she detects my presence. Which one should I harvest first?

I would shoot the boar first.  He's usually the most hesitant and learns the quickest.  Big boars get big for a reason.
I wouldn't worry about the pregnant one,  as long as you don't do anything absurd and she feels comfortable she should keep coming around.
Not sure how big the babies are,  but keep the dominant female for now. She's the one teaching the babies. 
The key is to befriend the babies.  It's easier to build a trust relationship with them and they will trust you quicker then the adults.  Once they trust you finish killing off the adults.
The current babies will teach the upcoming babies to trust you. 

At our spot the babies let us pet them and they eat out of our hands
When we pull up they recognize our car and come running down

Thanks that sounds like solid advice

Me, I don’t shoot small kine or sows with babies or if Hapai. 

150 pound female this past Sunday

Sent from my SM-G360P using Tapatalk

That looks delicious. Pretty good amount of fat too.

The thought of digging babies out also doesn't sit well with me either, but I was curious if there was a case for or against it.

Got some advice from a European pig hunter to start taking out the small ones first, or the male. The reason he gave was that the dominant female is probably the one regulating all the sex and if she's not there then the next generation will breed with each other like crazy. That might be more of a strategy for aggressive Russian boars that are larger and can easily overrun an ecosystem and even attack people. It sounded like an interesting theory though.

It got dark too fast this afternoon and I wasn't able to identify who was who (or clean shot), so I just observed behavior and it raised a couple questions.

Did some extra research when I got home and according to website below the Euro guy was right that the Alpha Female regulates the breeding of the young ones, not by physical cock blocking but pheromones. So if I take her out, the population would explode once the little ones reach sexual maturity and they would also be much more clueless and likely to warm up me

People who want to manage the numbers leave the alphas and shoot the piglets and young females since they are responsible for explosive reproduction. What I'm considering now is taking out the matriarch and getting the numbers up a bit, then going after the little ones on a regular basis since they taste better anyway. If I was on the mainland or Europe that approach would be frowned upon by responsible managers, but of course our pig breeds and ecological situation are a bit different here.

In any case this is some great reading about how control has failed in the United States and the populations are completely out of hand even with select fire, helicopter hunts, night vision, and heavily armed hungry rednecks everywhere

https://huntingboar.org/b/2014/04/07/the-role-of-the-alpha-female-in-a-sounder-part-2/

https://huntingboar.org/b/2014/04/29/the-role-of-the-alpha-female-in-a-sounder-part-iii/

https://huntingboar.org/b/2014/05/03/killing-the-matriarch-part-iv/

Finally decided to start popping the little ones first and got one last night. Regularly feeding them corn has a huge improvement on the meat quality compared to other boar I've had in the past. Roasted in the oven with dry rub for 5 hours at 275 and it was slightly dry but nice and tender and didn't need sauce. Now I'm hooked!

Would anyone in here offer this newbie to get a first pig kill? Would love to offer cash for a good day of hunting. I want to see how it feels to enjoy the happiness you guys have.  It sucks for me cause I want to try hunting I recently got my hunters card but no one to go with, plus my wife says I can’t go alone better safe then sorry

It usually takes 2 years to take your first animal. It took me 1.5 years for mines. In the meantime you learn stuff like, noise, movement, light, wind. Things you pick up after being out there. I hunt by myself mostly but I let my wife know where I'm going & about how I will be out. I also email her pin drops on maps or take her up there with me to show her where I will be. Also, learn the animals habits, where they bed, feed, water, travel routes. Not always easy but rewarding when you do. Happy hunting &  don't give up, it will come in time. Blessings, Alex

Ps, my first kill 4 years ago

Sent from my SM-G360P using Tapatalk