The smaller squashes, I simply cut in half, rub with olive oil and bake at 350 with the cut side down until a knife/fork inserted into the skin side easily slides in and out. Then I serve with a pat of butter, salt & pepper. Easy peasy.
Pie pumpkins will keep for a while. Obviously you can make pumpkin pies with those.

They also make tasty muffins, scones, etc.
The butternut squash will keep forever. Don't sweat that. I have bunches piled on my counter.
Cabbage - you can do something simple like cole slaw. I also make a vegetarian Colcannon in the colder months. Basically I just boil some potatoes and make mashed potatoes. Then cut the cabbage and steam it until it's a bright green color (be careful not to overdo it). Then stir the cabbage into the mashed potatoes. Sometimes I'll use a meat substitute like Wham. The kids even like it this way.
The greens are a different matter. Obviously you need to deal with those faster. I finally figured out that you can blanch and freeze these so I did that with my turniip greens and a batch of kale yesterday. There are some recipes on www.louisvillecsa.com that I like - Garlic & Greens Pizza is a favorite around here. Again, it's something the kids will even eat.
I can't help you much with the baby situation, lol. I used to wear my little in a sling to do most kitchen work (anything not involving a hot stove). Now she'll stand in a chair next to me and "help". Yesterday she was deveining kale with a butter knife.