I understand your dilemma (stress / time constraints). I don't understand you proposed solution (give up the longbow for a compound bow? "just looking online"). I don't understand what looking at a compound will do for your stress/time issues. If you don't have/make time for trad, you don't have time for compounds.
Do what you want. Have fun. If you can't shoot as much as you want to (for fun) or need to be (for skill level / strength), then consider dropping down to a much lighter , low cost trad bow (recurve or longbow). 30-35# will do. Shoot once a week. When live offers you a different set of options in a few years, re-evaluate your wants/ needs.
Life is hectic and stressful. Do things that make things less hectic and less stressful-whatever you choose. Maybe the answer is "put the longbow up for a few years until the next child is 3-4 years old." Life has cycles that wax and wane. Don't stress yourself out dealing with stress. If you don't find shooting relaxing at this stage of your life, remove it (for now) and get through this next stage. You'll know in time whether you miss archery (any form), or not. If you miss it down the road, resume it. If you don't, do something else. It won't bother me with either choice you make. Just don't be the type of person who states there is a problem, but does nothing to address it. Life is short. Keep it simple. Maybe you'll have a bigger driving force to approach archery (trad or wheels) with some time away from it. Maybe you won't. In 6-8 years from now, maybe you can teach your child (or children) to shoot trad. They will think you are the best shot in the world. Couldn't be a better feeling for a dad-if you ask me.