it's actually not so hard. just like everything else requires a plan. i've traveled extensively with just my kids when dh couldn't come with us and i really had it down pat:
bring the carseat on board. absolutely positively.
find a way to strap it to your stroller so that he can sit in the carseat that is strapped on the stroller. for my britax roundabout/pliko that was easy, it fit. for my roundabout in my venezia, it took a little more doing, but i made it work, i think i glued that sticky shelf lining paper to the bottom of the carseat so it was 'grippy', placed it forward facing on the arms of the venezia, then bungeed it in place.
i would have one bag to check
one carryon/purse (yes *only* one)
here's how it went at the airport:
dh pulls up carside, we all hop out. htere were also times when i parked b/c he was out of town. take out stroller, open it. take out carseat, put carseat on/in stroller in some secure manner (i have yet to find a combo i couldn't 'make' work). i would either put the carryon in the carseat or dd. whatever wasn't in the stroller, i carried (ie the *one* carryon)
i just put dd in the carseat and it was stable. of course i had to take her out to go through security, put the carseat through, fold up the stroller, put that through as well as the carryon, then i walked through holding her (and holding the hand of the other one once i had two....and yes, i've done it with two kids and two carseats

)
make sure not to wear ANYTHING that could potentially set off alarms (nothing metal *at all* b/c it's a pita to deal with that while holding/dealing with a toddler.
so open the stroller, put the carseat back in it, plop DS in the carseat swing the carryon/purse onto your bod and off you go.
once you get to the gate, approproach the counter and as for a 'gate check ticket'. they may give it to you then, or they may say that they'll give it to you when you're boarding (which is more often the case now).
when they call boarding, queue up (i usually wait toward the end-ish but i'm fast at installing carseats), line up with my stroller/carseat/child/carryon and head down the ramp. at the bottom, i take my carseat off and set it on theground...fold up the stroller, carryon on my shoulder/back, child etiher walking or in arms, carry carseat back back rim or straps (which mfgs don't recommend...by the straps that is).
find seat, install carseat. there's a trick. sit the carseat in the airplane seat, then *tilt the airplane seat back fully*, then thread the seat belt....here's trick number 1:if you click the buckle together and install it the regular way, it's easy...but at the end of the of the trip, when you try to unbuckle the carseat, the buckle that you're trying to 'lift up' will be going into the back of the carseat and it can sometimes (depending on the carseat) be almost impossible to get it open.....so to avoid that, before you buckle, flip the *female* end of the buckle over 1/2 turn...it's tricker to tighten it but you'll get it and at the end of your flight, it'll unbuckle easily so you can grab your child, your seat, your carryon and off you go. anyway, after you've flipped the female end 1/2 turn over, buckle the seat and tighten it as much as possible....then put your knee into the seat and bounce into the seat with each tug so that it's very tight. at that point, press the button to pull the seat back to the upright position and pull it upright (someitmes you have to ask the person behind you to give a push to get it upright)
when the flight is over, take ds out of the seat, unbuckle it, grab your *one* bag and you're ready to go. you deplane and wait right by the door of thhe plane (or whereever they tell you) for your stroller....set up the stroller, put thhe carseat in, ds in the carseat and the bag on your shoulder.
easy breezy!!
even when i was alone i could do it (what a sense of accomplishment!) i could push a stroller with one hand (with the carseat and carryon in it) carry dd in the sling (on my back or front) and pull a full sized wheeled suitcase with the other hand.
i also carry hand sanitizer and handsanitizer wipes (the alcohol ones, not the chemical disinfectant ones). when we're on the plane and settled, i wipe eeeeverything down with alcohol wipes, then babywipe our hands, then hand sanitize with alcohol hand sanitizer.
i carry the little bottles in the park on the girls tiny fanny packs and my backpack. i also carry an 8 oz bottle for when we're all doing it at the same time....we go through a lot of it

i also bring a refill full sized pack of babywipes b/c i go through a lot of them when traveling....you can see my post under 'is this true?" to get an idea of how i keep our room clean-ish
katherine in atl