There may or may not be a 2nd scan at the point that the FP and standby lines merge. Anyone in the FP line would scan whether using FP or DAS.
I recommend that you go through the line and approach boarding in pairs based on who is riding with whom. Some ride vehicles may fit your whole party while others will seat 2 or 3 or 4, some are continuous moving and will not give you a lot of time to be "handing off" various kids so you'll need to trust the teens/nanny to manage boarding with their "assigned" kid(s) including assisting the child with transfers. I recommend you watch some
YouTube videos to get an idea of ride vehicle size, loading process, and timing.
Keep in mind that DAS is a service providing access to queues. It has no other "power" at boarding or for seating or such. If you end up with 2 DAS, your party will be split as "riding with" one or the other of the girls at each attraction you use the DAS. If you need moving walkways slowed or other requests, you (or the adult/teen with that child) will need to mention such request at the ride or even along the queue.
As for "slow" times - those really don't exist at WDW anymore. I believe you mention that you were last at WDW maybe 8-10 years ago with DS. Much has changed in that time and crowd levels are one. Crowd calendars are a great tool, but keep in mind the crowd levels noted are all relative. Dates noted as "low" are smaller crowds than moderate or peak times, but should not be interpreted as quiet or slow or few people. I would guess that late Jan/early Feb is the least crowded time of year, but many who are familiar with that time of year will agree crowds are bigger now than even just a few years ago. You also run the risk of attractions offline for maintenance.
I commend you for taking on such a trip and wanting to provide the experience for your family. I just remind you to keep expectations in check. There have been lots of mentions of this possibly being a once-in-a-lifetime opportunity, family staying together, riding together, don't disappoint, etc. WDW has a great reputation for those with disabilities, but not everything will always be possible.
Enjoy your vacation!