It is indeed the Guest Relations kiosks. And no, you cannot do it at the attraction entrance - it causes too much backup and crowding issues, hence the Guest Relations kiosks that are set away from actual attraction entrances.
There are two different systems. At new parks like DCA, all attractions/queues are accessible to wheelchairs, ECVs, etc. So the DAS card is primarily for guests with cognitive disabilities who have a difficulty with waiting in crowded conditions. The return time allows the quest and party to do their waiting outside the queue, but for approximately the same amount of time. This is the system that gives return times at the kiosks.
At older parks like Disneyland Park, there is the additional option for guests who have an assistive device, such as a wheelchair, ECV, crutches, brace, or (in my case) artificial leg. Guests with physical disabilities who are using an assistive device can go to the attraction entrance and ask how to access that attraction without a DAS Card. The Guide for Guests with Disabilities gives clues on what is appropriate for each attraction. You may directed to an alternative entrance or given a return time equal to the posted wait time. But this can vary according to the conditions at the time.
Older attractions at Disneyland have different accommodations, which may vary according to how busy the attraction is. DO NOT assume you can waltz in through the exit, even if you have been there before. Do the cast members the courtesy of asking at the entrance. At some attractions, like Pirates and Mansion, working the wheelchair line is hell on earth during peak season. Haunted Mansion is limited by the Fire Marshall to three wheelchairs/ECVs/Service Animals in the building at any time. If you can park your chair at the entrance, do the people who have to transfer in the load area the courtesy of doing so. Also, if you need to have the load belt slowed, have other members of your party go first and alert the cast member--they will be happy to do it and call Unload to slow for you again.
I have had many friends who were attraction cast members and I know people who have left the department SPECIFICALLY because of the stress in dealing with the wheelchair line at an older attraction. Plan ahead and be prepared for wait, JUST LIKE EVERYONE ELSE!
There are people, including those with fragile health and cognitive disabilities, who have difficulty waiting. If I'm going to spend a full day in the parks with my nephews, I sometimes bring my wheelchair just so I have a place to sit down. I use my fastpasses, but sometimes (Toy Story Mania) we just have to wait. I can outwalk the kids on my hi-tech prosthesis, but standing kills me.
Don't make assumptions, and check your sense of entitlement at the gate. A DAS card is NOT a front-of-line pass. It's not a "Willie Wonka Golden Ticket". It's not a benefit we receive for having a disability. It's a tool to assist us in enjoying the parks
the same as everyone else, not better than everyone else. Also, the DAS card is for attractions--NOT parades or shows. Sometimes there is a special section for wheelchairs so they can see and not be trapped behind the crowd, such as F!, WOC, and parades. There is NOT a "reserved section" for people with disabilities.
I don't mean to sound like a scold. But I have heard horror stories of the minority of people who try to "game the system" and make it worse for people with disabilities. They have clamped down at Guest Relations. I can no longer get a DAS Card after years of using one. But it's survivable for me and my family. Sadly there has been a lot of abuse of the system to the point that it became unworkable. This includes people with DAS Cards (and the more lenient predecessor GAC) who rented themselves as Tour Guides with "front-of-line" access. If you go to Guest Relations, be very clear about what type of assistance you need to be able to access to the attractions.
The system is not perfect, and it can be uneven in its application. But cut the front-line cast members some slack. They're doing the best they can for less than a living wage. If you have concerns, go to Guest Relations and be specific about how you feel the system isn't serving your needs.
I've been using the various accessibility methods for decades, starting with renting a wheelchair for my grandmother when I was a kid. I have used different aspects of the systems with various friends and family members. I have been involved in disability advocacy and support as a person with both visible and hidden disabilities for over 20 years. We absolutely need to keep Disney working towards greater accessibility for the foreseeable future. But you need to understand what is actually being offered and why. You and your party will have a more enjoyable experience if you plan ahead and know the limits of the system.