No, you're not bonkers. Make sure you have plenty of bribes and distractions. If you get delayed for an hour or 2 it helps to be self sufficient.
My Bushbaby is too big to have as handluggage. You should be OK with your buggy as far as the gate but, as Buster says, where you can pick it up from is more a problem. I did over 30 flights with ds in his first year and there was never a consistent policy on where the pushchair would be even on the same flights.
Your 3 yr old can take his own travelpack which should make them feel all grown up and most of their supplies can go there. I have a small drawstring bag that fits on my shoulder that I keep in my hand luggage that I use to contain 'expansion' aquired at airports like bottles of water and newspapers. Make sure you take some supplies for yourself in case you get delayed, it's easier to keep your cool if your bloodsugar is not dropping.
If you are travelling with a budget airline you prob will have to pay extra for special assistance. If your seat is not reserved you should be allowed to board first to bag your seat. I wouldn't necessarily go for the front row as you can't always have keep bags of tricks around you during take off, which you will need to keep you all entertained. I hate that bit after boarding waiting for take off it's so difficult to keep children still.
This may be the time to consider getting a Hippy chick belt (or borrowing one). If you end up having to carry your hand luggage, control a 3 yr old and carry a wriggly 10 month old then you will need all the help you can get. Your other luggage should be less of an issue as it should be easy to get hold of airport trolleys.
On the bright side, if it is a seat free for all and the flight is not fully booked, you will prob get the third seat for your baby.
Allow the same planning for the return trip when the thrill of anticipation has gone. Get dh to pick you up from the airport.