I agree with the other few PPs who have pointed out it's not that far and you're focussing on the wrong problem.
Pushing/dragging two bulky things is no fun, so ditch the scooter and get a buggy board. But why is DD so tired? Is she sleeping badly? (Can you do anything to improve her sleep routine?) Is she generally unfit? (Can you do incorporate more gentle walking/energetic play on your OH's days off, so there are two of you and you can split looking after the kids so you're only looking after one at a time?) What is she like on the way home? (Presumably you have to make a return journey - is she OK on the way back or is she equally/more tired?)
What about you? Are you tired from lugging around two bulky things, or are you tired before you start the trek? Improving your sleep as a parent is difficult, but is there anything at all you can do to help yourself cope with mornings better? You may have already optimised your morning routine, but is there anything you rush around doing in the mornings that you can skip/do the night before? Is your OH disturbing your sleep routine? If so, can you try temporarily sleeping apart just so you get to feel a bit more human?
You say your baby is tiny - did you get a chance to fully recuperate after the birth or are you actually still recovering? If you've never really healed up/rested properly, there is no shame in saying you've put your body through too much and you need a rest break. If you went from childbirth straight to running around after two kids, it's no wonder the cumulative exhaustion has got you.
I know it's a lot of questions and I don't expect you to reply, but I'm just trying to get you to look at the situation from a different angle.
Driving lessons don't mean you'll definitely pass and getting two kids in and out of a car in a hurry isn't particularly fun, especially when you add in school drop off madness. You're trading one set of problems for another.
Take a step back, identify all the causes rather than just the symptoms and look at what you can make better. If you really at breaking point, rather than get a taxi, some paid childcare on a temporary basis might make more sense.