Security lines can vary in length and time. We typically don't visit during high season, so I can't really speak to what lines are like other than when we go (typically Jan/Feb and late Sept/early Oct). We also tend to let the crowds get ahead of us for rope drop, and rarely arrive before 10:00 to 10:30 am, so lines tend to move fairly quickly for us. If you are there on the weekend, however, all bets are off; lines *will* be longer, and especially for MK.
Last time we were there, the security officers at bag check were dressed pretty much like a police officer you might find in any city; they are obviously there in a security/law enforcement type capacity. I don't know how your children respond to setting expectations (Before you leave for the trip, "We are going to see some security officers when we go into the Park, but they just need to make sure everyone is safe, and we can help them do that by good girls!" and then continuing that same dialog literally through the entire trip) but I know that security/bag check can be a "pinch point" for some folks.
Have you taken your kidlets to a local fair or amusement park? How did they handle that kind of environment? And, just as importantly - how did YOU handle it? My concern is not for your children - you are obviously a loving and adventurous mom! - but for you. You will be there all alone, and although I can tell you are NOT shy about taking your littles out and about in your hometown, this *is* different.
For healthy parents & kids, Disney World (and vacations in general) come with a LOT of emotional baggage, as well as taking a physical toll. Factor in any physical challenge(s) you face, plus the challenges your children have, and you are carrying more than any one parent alone should try to. I know - believe me, I understand about family members who just seem to make things worse/harder than it has to be/the queen of snarky, useless comments (who can't be bothered to do anything *actually* useful, but sure has a comment for every situation!) and I think I might have walked near your shoes, if not in them.
I'm not saying you HAVE TO take another adult with you, but is it possible to identify just one other adult who could actually be helpful? My concern is for you - if something were to happen to you, and you needed some medical attention (maybe you strained your back) how will you cope with both girls, the stroller, and everything else by yourself? I know you aren't "fragile" - obviously far from it! But I also know that there is a certain emotional cost to trying to do everything by yourself, and that can sometimes spill over into a physical cost as well.
I'm NOT trying to tell you to not take the girls - I'm just concerned about you. It's so easy to get caught up in the "perfect vacation" syndrome with a WDW trip; you want everything to be just like it is in the TV commercials, and then the reality is always hotter, sweatier, busier, and far more physically exhausting LOL. Without another adult to give you any kind of a break at all, without any backup, I fear that you won't really enjoy this trip as much as you think you will. And it's supposed to be your vacation too.
I don't know how old your girls are - or what their capacity for making memories is, given what you have told us about their condition. I can tell that taking them to WDW is very important to you, just as it is for so many parents; we want to share that Magic with our kids! If waiting a year or two means that all of you will have a more enjoyable vacation trip, you might want to take that into consideration.
Only you know your children well enough to decide if this trip is right for them - just make sure that it is right for YOU too. You deserve to have some Magic as well, and I hope that's what you find!
