Hiya OP.
I have suffered with serious depression for years. Have started exercising in fits and bursts over the years, but never kept it up. Like you work, small children, a health condition and low mood/low confidence always stopped me in my tracks.
I decided to give it a proper go again three weeks ago. I joined a low cost gym and decided to commit to going three times a week for 45 minutes each session. I was terrified the first time I went in and felt self conscious and pathetically unfit and just scared. I started with a couple of sessions where I just walked on the treadmill and did some very light weights, and realised I felt a lot better after this. I then braved a yoga class....then a stretch & tone class...then then a body combat class. I went five times the first week (who me? The gym phobe?!) and within that first seven days, I felt SO much better about everything. I WISH I had taken the many people who have said to me over the years 'exercise improves mood' more seriously years ago!
Three weeks of going four-five times a week has reduced my anxiety hugely, cleared my mind quite a bit (less of that mentally fuzzy, 'walking through treacle' feeling I suffer from). It has made mornings easier - I have more energy and dont wake up feeling that awful sense of dread I have lived with for years. It has also had loads of other positive knock-on effects. I'm drinking less booze, eating better, feeling more sociable and it has given me a huge boost actually deciding to do something and then sticking to it this far (OK its only three weeks, but thats huge for me!). Its been the best 'medicine' I have ever taken - better than meds, CBT, mindfulness etc. Seriously.
My advice would be:
Identify the time you are free to go to the gym each week. Be assertive about arranging this 'me time' with your DP/DH if you have one. Or get the childcare sorted. Then write down in your diary (or i write it on a piece of paper and stick it on my bedroom door) the days you are going to go and GO on these days. I tick off each time i go and its great to look back and see what you did the previous week and feel pleased with yourself.
Stop viewing it as a chore or something you 'should' do because its 'good for you' and start to reframe it in your mind as a luxury, pampering thing. This is something that is going to be GREAT for you. Its going to make you feel better. It will be tough at first, but you are quickly going to start finding it easier and/or enjoying the buzz of setting yourself small goals in the gym and reaching them.
See if you can find a gym really close to where you live, so that the journey is straightforward.
Have an induction at the gym so you know how to use the equipment and are familiar with the layout. Makes it all less daunting.
Google a basic beginners gym routine and try it out. I do 10 mins treadmill, 5 min deep stretches, 20 mins weights, 10 mins treadmill again. Cardio/stretching/weights is a good basic rule of thumb for improving overall fitness and getting your whole body feeling better.
Mix up gym session with classes. I get bored of the gym and can only manage two sessions a week, but i am having fun trying out new classes. Some of them have been tough (I'm usually the red faced breathless mess at the back of the class!), but at least I'm not bored.
Good luck! It has already changed my life in such a short time, I cannot tell you x