We've done a few things to minimize the constant busyness. My husband and I both work full-time, although right now we're both off work due to the birth of our 3rd child.

For us, the biggest roadblocks to relaxation are dinner and cleaning. We've decided that our house is clean enough if we do cleaning just once a week. It typically only takes a couple hours and we're good for a week. We do a quick toy pick-up periodically, but that takes less than five minutes.

We have a system for laundry. Each person has a basket for their dirty clothes. When that basket is full, that person's laundry gets done. It usually takes about a week or so for each of us. This system makes the folding/putting away part super easy because there's no sorting to be done. My husband does his and my son's, I do mine and my daughter's. The newborn's clothes will probably get tossed in with towels or something (he's so new, I haven't worked that out yet).

As for cooking, this takes some preparation but is totally worth it. Every couple months, I make about 30 or so (near)complete meals and put them in the freezer. They are typically for the crockpot, so they just need thawed and tossed in the crockpot in the morning. At dinnertime, steam some veggies or whatever if needed and you've got dinner. The preparation for 30 meals usually takes me about 6-8 hours.

It's definitely challenging to find family time. I expect we'll need to make adjustments due to adding a third child. The bottom line is, all the things you listed as time drains have to be done, but you and your wife need to decide how often and how well. We're willing to let cleaning slide a bit, it might be something different for your family. Family time has to be made a priority, otherwise it does tend to fall by the wayside.