Do whatever it takes to handle things, but for this:

> My wife and I BARELY have time to go grocery shopping

If you can, take them grocery shopping with you. One parent stays at home doing stuff, the other goes grocery shopping with at least one kid.

In my experience kids at least 12-18 months old LOVE grocery shopping.

Get a big shopping cart, put them in that special seat facing you. Keep it concise, don't shop for more than 1 hour per round. Talk to them, explain what you're doing, give them harmless things to play with (a carrot, a celery bulb, a bag of rice, whatever). Have a little fun with the produce, they will love random things, for example that weird looking tomato.

It becomes even easier as they grow a bit.