Ewemoo Please also post feed amounts for them. This will help me in looking at the whole routine properly. I can see a few things in your routine that can be tweaked. If I read correctly here is what you are doing.
5.30a Feed (how much?)
8a Awake
9/9.30a Feed (how much?)
11a-1p Nap
1.30p Feed (how much?)
4.30p-5p Nap
5p Feed (how much?)
Bed time (When?)
1.30a Feed (how much?)
Here are my suggestions assuming you are doing an 8a-8p day. I don't know your bed time.
5.30a Half Feed
8a Woken up
8.15a Half Feed. Feed them even if they are not very interested. Even a little feed of 2-3oz may help with the irritability during the school run. They will not be very hungry at this time since they were fed twice in the night. Mine have the same problem. I get 3oz down them so they last until their nap.
10a Put them down for a 30mins nap once back from school run. If you have to do a top up feed to lull them into sleep then try that. Being outside is exhausting for little babies. If you put them down before they are overtired then they may settle better.
12p Full Feed. Move the 1p feed forward. Also if they had a nap at 10a then they will last closer to noon or even past it w/o being grumpy. A good feed will ensure a better nap.
12.30p-2.30p Nap. They may wake up before but try to resettle them with half feed if you can. Keep things quiet and draw the curtains so that they room is not too bright. Keep an eye on the temperature. Tuck them if they like that with a thin cotton sheet. You can tuck the sheet under the mattress on 3 sides and then use rolled towels between the cot and mattress to pin them down. I find that mine sleep better tucked in. They always hated being swaddled.
2.30p Half Feed. Feed a little before the school run. I would ideally feed them at 3.30p but your school run would prevent this. So may be try to give half feed before and half after.
4p Half Feed. Give remainder of the feed after school run and lull then into a nap of 15-30mins.
4.30-5p Nap.
6.30p-7p Feed. If you have the energy then try a bath before this feed. Mine always settle well if they have had a bath before bed time.
8p Settle in Bed.
You mentioned that sometimes they don't do a 2hr nap midday. If you are not able to settle them back with a feed then try to lull them into sleep after the 2.30p feed. May be you can do this in the car seat so that you dont have to move them for the school run. Then try to see if they will have a second nap for 30mins or so before the bedtime feed. You must try to have them sleep closer to 3hrs at this age broken down in to 3 naps. Some babies will normally sleep longer at lunchtime and some won't. Yours seem to be able to do a longer nap. So it might work to your favor to establish that so that you can get some downtime.
Thats all I can think of now. Good luck!