I know about the car seat having to be in the window seat but a question just popped up for me... what would an adult flying on their own with two children in car seats do? Surely they would not make the adult put one of their children in a window seat next to strangers somewhere else on the plane, would they?
If you have one adult and two carseats, you may place the carseats next to one another, with the larger at the window and the smaller in the center, if they are different sizes. (FYI: Delta FA's have been known to allow people in this situation to sit between the carseats, though technically that violates the rule of not placing the carseat where it "may impede egress.")
There is a real exception to the window seat rule, *if* you are traveling on a widebody with two aisles. In that situation, a carseat may be placed in a center seat of the center section. (With two aisles, you are directed to evacuate via the one closest to you, so no one would need to climb over the seat to get out.)
Another important rule about placement: Carseats may not be placed within one row's distance of the emergency exit. This means that they may not be placed in the row directly in front of, or the row directly behind, the exit row. If seats are pre-assigned in either of those rows, call and try to get them changed before the flight.
Also, regarding getting to the gate: Yes, you *can* have someone you know accompany you if you really need help. Airlines are allowed to issue gate passes for non-flyers who are needed to provide special assistance. The helper goes with you to the counter, shows ID, and asks, and if you clearly have too much to handle on your own, you can usually get a gate pass for the helper. However, I really don't recommend this if you are not being met at your destination, because you have to get off, too, and it is best to limit yourself to what you can handle without help, if that is possible.
The key to dealing with kid paraphenalia in airports is to have the right gear and use it efficiently. Invest in equipment that is meant for travel. Kids who can walk should wear their own toy backpack, and the diaper back should be on your back, with a spare change of clothes and your purse essentials in it. No other carryon bags. If you are using a backpack carseat satchel, put your diaper pack in it until you get to the gate. I've found that while airline employees are not allowed to secure the carseat(s) for you, if asked, gate agents can usually arrange to have someone take the seats onto the plane and set them down in your seats, so that you don't have to maneuver them onto the plane. (SWA will often have someone available who can help you preboard, at least to the point of carrying the carseats for you.)
None of this is going to happen if you don't ask, but don't demand it, either: attitude is everything. I've always had success when I ask nicely and make it clear that I am asking in order to make boarding go more smoothly. (On an flight that has 1st class seats, it usually doesn't hurt to mention that you are concerned about accidentally hitting seated passengers as you try to board with those unwieldy carseats.)
BTW, I'm not a nazi about anything; as long as whatever you wish to do is legal, then feel free to do it; they are your kids. I personally found that keeping squirmers in their carseats was easier on me during flight, and since carseat use is recommended by aviation authorities and guaranteed if the seat is approved, I chose to always use them (and always was pretty often, as I fly a lot.) To me, the logistics of transporting the seat did not outweigh the advantage of using it on board. Once I got the hang of tricks to make transporting seats easier, it ceased to be an issue in my mind. I also insist on gate-checking older childrens' carseats to be absolutely sure that they arrive when I do, which again, is my choice.
(Edited to correct an unclear sentence.)