I am a little confused by your questions but I will try to address some of this as I am "perceiving" what you are trying to ask.
We would like to be involved in rescue, working directly with a mill to save their unwanted dogs, rehabilitate and rehome them one or two at a time.
The reason that you become a 501(c)(3) rescue is to become tax exempt for donations to your rescue. Rescue take in donations and also charge a rehoming fee to help to recoup the money that is paid for vet care of their rescues. You need to contact the Secretary of State in your state, make sure that you will qualify, follow the rules and apply.
With that being said, I do not think your idea is not totally out of the question but you do have several obstacles associated with your objective. I do not believe that rescue should go to the mills to "save" dogs. There are plenty right in the shelters that need to be saved, some even from the mills and I suggest that you start there. Build a relationship with a local shelter that is known for having puppymill dogs in their care.
Many shelter will also allow a rescue to "pull" a dog without paying the charges that the public would be charged if you are a 501(c)(3) organization in exchange for taking care of their medical needs. A mill will not (likely) just give away any of their dogs to a rescue. They will lay on the guilt to squeeze that last dime out of their stock.
You need to anticipate that a mill rescue will come to you most likely having no house manners, frightened of humans, needing to be spayed/neutered, vaccinated, dental, heartworm positive, and those are the lucky ones. Many have genetic issues like severe LP which can cost thousands to fix. They will most likely have many if not all of their teeth infected and might lose many during a dental. These dogs are usually a mess and have huge medical bills and are emotionally scarred. You will need funds to pay for vetting, possibly thousands of dollars to care and rehab a puppymill rescue prior to having a dog in your care.
Which leads to your other question about adoptions about making it difficult for adopters. After spending hundreds or even thousands to rehabilitate a dog you too will want to raise the bar to make sure that they find a permanent forever home. I really do not think that rescues make it hard to adopt to be mean, they really want to make sure that after all that their rescue have been through they will forever have a home and be loved the way they should have been all their lives.
In conclusion, my suggestion to be to:
Research 501(c)(3) in your state. Go to your Secretary of State website and get all of the rules that will need to be followed to be granted a 501(c)(3).
Gather your funds to pay for vetting.
Get your message out. Begin a dialogue with shelters in your area to call you when they have a mill pup surrender. Search Petfinder.com for pups in your local shelters that are mill surrenders.
I wish you good luck with your ideas and congratulate you on wanting to help the cause.
