to sk for advice on fitting in exercise?

[DrSeuss]

Posting here for traffic.
I need to lose weight and have been trying hard to do so with some success and a few wagons fallen off. That bit I have in hand. However, I also need to get a lot fitter.
My problem is, my daily schedule. I am not making excuses, really I'm not. I struggle to fit exercise in.
6.30 Wake up. Always knackered due to insomnia
8.00 Leave house, having first done some house work and got self and kids ready
8.15 At work
3.20 Finish work. Sometimes I get a fifteen minute morning break, sometimes I don't. (I'm a TA. That's just how it goes.) once a week I have a break duty. Lunch is 45 minutes in theory but I rarely get all of that. Twice a week I have a dinner duty, so only 20 minutes for lunch.
From work, I go to pick the kids up and then they have activities every night till at least six. Sometimes I can take a walk while they do their thing. Some activities require me to stick around just in case.

6-6.30 - Home, cook, homework, reading, spellings etc
Sometime between 7 and eight or even later, husband comes home from work.
Weekends are kids' activities and housework and just trying to have an actual life!

We have no family to help out. It's nearly all up to me. We can't afford endless babysitters or a cleaner.
So, how can I fit more exercise in?

Cycle to work? 15min tabata/HIIT

Running maybe. Depends on the activity as I have no intention of running round the industrial estate where a couple of the activities happen after dark but for some I could.

In a few weeks it won't be dark. Ok it's not going to be the prettiest running venue, but it's easy.

I've just started focus T25 It's 30 minutes with the cool down. I started noticing small changed quite quickly even though I'm not doing the diet that goes with it.

Youtube is a great thing for random exercise videos - you can see if there's any trainers you like before spending money! To feel like you're achieving things there's a variety of 30 day challenge apps. I like the squats and abs ones that have basic blue graphics and 6 levels. Less convinced by plank and push ups because they progress faster than I'd ideally like so I don't get to tick things off. They shouldn't take long to do.

I do like running, including in the rain - much nicer than hot sunshine!