I've had days like you describe! My DD is 3.5 and my DS is almost 11 months. Especially when I was on maternity leave, I really beat myself up about how long it was taking to get ready and the state of the house. I started back at work 4 days a week in August and I still struggle to get us all ready, them dropped off and me to work by 9am. I thought it would take a couple of months to speed up and feel in the swing of things, but I haven't really and I don't really! My house still isn't the cleanest, but the kitchen is tidied and wiped down every night, toys tidied before bed and downstairs is hoovered regularly. The rest gets done when anyone is coming round!
From experience, the night before is key - I try to have a bag packed ready with nappies etc, an empty cup, some breadsticks, a bib, and a spare outfit for DS; coats and shoes all together in an accessible place; and lay out all of our clothes so I'm not rummaging through laundry or ironing in the morning! Decide meals for the next day and put anything that'll need defrosting in the fridge.
During the day, I think we have to be realistic about what's going to work. If your LO's nap is making mornings too short to get ready and out, maybe decide to stay indoors and play each morning, and snatch moments when he's in his highchair or napping to put on some washing, load the dishwasher, empty the bins, hoover a couple of rooms etc. Big jobs can wait until he's in bed or you have help!
One thing I've learned from my in-laws who have retired this year is to assign activities to some days of the week to give you structure: Get timetables from Children's Centres, swimming pools and libraries and see what is age-appropriate on which days.
We take the kids swimming on most mondays and that's the day I go supermarket shopping, my in-laws take the kids out for lunch to a Wetherspoons with a family area every Tuesday morning followed by the park, Thursday and Friday the kids are at nursery and our gym does kids activities on Saturday mornings.
I've recently made a list of activities for my kids from a book that I've stuck to the fridge and I pick from the list if I run out of steam!
Writing this makes me feel more organised than I thought I was... I think we're all probably doing a lot better than we think we are, it's all a matter of perspective and a few little tweaks!