I was about to state here that in your case cycling to work may not be worth it because you won't be able to spend as much time with your family. However, since you have shared your health concern and seem determined to achieve a healthier lifestyle, I think this is actually doable as long as you try to strike a balance between driving and cycling. Leebo's suggestion is actually very clever and easy to implement, and I'm sure that following such a middle-ground option will enable you to both cycle more and remain healthier, as well as still be able to spend as much time as possible with your loved ones.