Codependency Support Group
Codependency is defined as someone who exhibits too much, and often inappropriate, caring for another person's struggles. A codependent person may try to change, or feel shame about their most private thoughts and feelings if they conflict with the other person's struggles. If you are on a journey towards self-love, this support group is for you. Join us and find others...

The secret to happiness is to be content with whatever is our circumstance.
Seems to me that you would be getting plenty enough exercise by chasing after the 2 babies. You have simply changed the type of exercise.
I like the way you divide your old self from now your new self, because I see that as one of the coolest things in my life, in that long ago I use to be an Electrician, and another job as a Carpet Cleaner, and was a truck driver for about 5 years, and long ago I was married for 5 years, then later another relationship for 4 years, and then being single for 10 years, and so I see my own life as divided into different sections which the different parts make up the whole me.
The idea that you could stay the same for your entire lifetime seems kind of boring to me, and I know a lot of people who just do not want any kind of change as if they do not want their life to be an adventure - as I like mine being lots of different adventures.
Our old self is our foundation for our new self, and so I say to embrace it as being fun.
I use to be young, use to be healthier, use to be so important, and now I get to unwind down as I get older and older.
Our self care just changes without ever going away.
Welcome here to this group.
EDIT: One thing I did when I had 3 kids under 5 years of age was get them on a sort of schedule. I was not overly rigid, or mean, but they had a set bedtime, we ate at set times, nap after lunch, baths after dinner and winding down with books to go to sleep. We ate dinner fairly early and simple to cook and clean up meal, so that I could have the kitchen cleaned up and then do baths and then bedtime and then free time. My ex husband did not help at all. This allowed me time to do self care because I was not allowing time to fritter away and it gave me a sort of goal to aim for.
Exercising is not the only way to self care. Seems like you are tired and overextended. Perhaps instead of focusing on exercise, you do some easier self care practices. Such as....when the kids sleep...do your nails, give yourself a 10 minute pedicure, make yourself a nice cup of tea and maybe a dessert just for mom...and read 10 minutes of a good book. Maybe you can light a candle and meditate for 5 minutes, or treat yourself to something you've been wanting for awhile.
Self care is anything that makes you feel good...whatever that is.
I think it sounds like you've lost your identity. My best friend went thru a similar situation after having her first son...all she was was mom...and she forgot herself.
So her therapist suggests doing activities that she did before the kids and husband. So she's writing music again, talking to old friends, buying herself better clothes rather than mom sweats, treating herself to a glass of wine. These things help remind her of who she was. I think than can help you...focus on regaining your identity before the kids.