I highly recommend the mommas heating pad / cave, or, an adjustable height heat plate.
Not one that gives ambient heat from a vertical position, but one that the babies can stand against/ snuggle under, and you can adjust the height <- very important, regardless of your decision 😊
As for your coop, there is a whole section filled w ideas
I am sorry I’m not sure how to send that link, maybe someone here can help?
However, I will say, that if you are sticking it into that side yard.... you will want 1/2 - 1-4” hardware cloth on the fence (depending on your local...
I think the crate looks safe from.... most things.
But. The babies will fly sooner than you might think...
You might consider this as a safer option than the heat lamp....?
Momma heating pad
(I use a long heating pad on the top, a short one in the bottom, and have some leftover heavy fencing...