low impact suggestions on busy schedule

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I'm nearing 40, I think I'm pretty unfit, I cycle most days for about 15 minutes but other than that I wfh and very sedentary. I'm after some suggestions for exercise around a hectic schedule. My BMI is ok (I'm 8st 7 and 5ft 4) but I am not healthy as this is mainly managed through (an awful) diet.

I have severe back issues, and orthopedic consultant advised not to do any jogging or high impact exercise due to a congenital issue with my spine formation and it is highly prone to early disc degeneration. So obviously I decided to ignore this thinking that after 20 years it wouldn't matter and start couch 25k this week, I am now in agony after 2 runs, my lower back is spasming, I've lost feeling in my legs again and I've had to jump back into my box of pain meds. I tried to be careful, lots of warm up, good shoes, treadmill but I just think the pounding impact is too much. To throw further spanners in the works, I also cannot do any exercises that involve crunches/sit ups or extending my back. A cobra pose in yoga will 'slip' my disc for example (I have learnt after bitter experience!) Anything that involves my lower back twisting or folding in either direction is bad news, so past attempts at yoga or pilates have usually ended with hospitalisation.

I have to work at least 50 hours a week, although mostly wfh, I have two young dc, so I tend to wake early (4/5am) to do work before they get up, do school runs, then work until 2.45, more school runs 3.30-7pm spent with them and then start work again at 7-11pm to make sure I'm doing enough. This means that external fitness things, like joining a gym or swimming are out too. I could probably fit in outside exercise between 3.30-7pm but would need to take DC with me or do it in the garden.

Are there any magical suggestions for what I could do to improve my fitness? Are there any video plans of low impact exercises anyone can recommend? I realise I should perhaps be doing weight/strength training but no idea with how to begin with that either. Help!

Waking walking walking.

Swimming?

Jo Wicks has low impact HIIT for free on you tube but sounds like that's could be too much for you. He also does chair based exercises which are aimed at older / immobile people but could be a way for you to build up.

Actually I'd look at your work, why 50 hours? How old are your kids?

DC are 6 and 2. Workload is just a lot and I need to put in the hours to ensure I'm producing enough to keep up with child free colleagues.

Walking is the lowest impact you can do. With regards to strength training I would personally try a physio led Pilates class where they know of your issues and stop you from getting injured. This will help longer term with your back.

I would say a cross trainer is lower impact than walking as you're just moving your legs around not actually lifting your feet up and down. Likewise cycling - could you put your bike on a turbo trainer at home?
In terms of weights I'd get some proper advice from someone who understands your back condition or you could do more harm than good.

Check out Joe Wicks YouTube channel. He'd just done some workouts called "First Steps to Fitness" which would be great for anyone just starting.
I have recommended them to someone else as well (I watched the first one through to see the exercises).

Les mills on demand, they do a 3 week beginners low impact plan- "journey to health"
Almost finished it and really enjoyed it.

Jessica valant pilates. She is a physio and has loads of spinal safe pilates routines.

I’d just stick with walking for now and pick up something else later when the children are older. You’re young, you don’t need to panic. Walking is something you can do as a family.

Depending on budget can you get a walking treadmill - just the type that can fit under a desk/table and walk while you work?
Could you do a ten minute walk building up to fast walk either side of the school run?

I would put the 2yo in the buggy and walk for an hour after pickup. As he/she gets older and heavier you will get fitter. Can you get your partner or a friend to babysit 2 evenings/week (one on a weekend) so that you can train at a gym with a PT with weights? You also mention that your diet is awful. Maybe look at improving it with lots of protein, vegetables and fruit.

Sorry I didn't come back to this. I can't do evenings as I need to work. I've decided to try and get both DC cycling and use the weekends more. Diet is better this week, cleared out the cupboards and made some soups for meals.

I feel like weights would be a good idea but without any break from work or childcare I can't work out how unless I just lift DC?

I'll look into the treadmill, thanks! School run is usually a desperate dash back to get on a meeting. Pm one is better but DC often need ferrying to clubs.

Another advantage to doing family walks is the increasingly recognised benefits of being in nature for both physical and mental health, which I really don’t think you’re going to get trying to do something at home, especially as you work from home.