Stay-at-Home Father: Fulfilling Time-Bound Positive Commandments

I know women are exempt from time-bound commandments in part because of the need to provide childcare. But what about a man who is the primary caregiver for his children?
My situation is that I am a stay-at-home dad and I probably will be for many years to come. My wife has a very demanding job where she is away from home for as many as 14 hours a day. After having our first baby recently, she had some maternity leave and this freed me up some time to do things including davening. Now she is back at work and except on weekends, I find davening at the proper time practically impossible. Childcare is much more of a responsibility than I ever imagined. It’s much harder work than the full time job I had before our daughter was born.
Even before we conceived, my wife wanted me to quit my job to be a stay-at-home dad as soon as we had children. She made it clear to me that she prefers work to childcare, and I love children, so it is a good arrangement. I gave my notice two months before the baby was born and stopped working six weeks before her birth. I’m glad I did because I was so busy preparing for fatherhood even before she was born. Now that I am my daughter’s primary caregiver, I literally have no free time except maybe a little on weekends.
This is just the beginning. We want to have more children in the future. This puts me in the position of being primary caregiver of the children for decades to come. I will always be the one who feeds them, changes their diapers, does the laundry and housework, and takes them where they need to go. Which means I can’t see myself being able to daven at the proper time as hard as I might try. I do very much love what I am doing, but I am feeling guilty about not davening.