Chickens aren't cuddly wuddly creatures towards each other and new "interlopers". The pecking and picking is normal.....albeit not ideal
I try to raise "large" batches of chicks because integrations are a lot easier. When dealing with small numbers....1 or 2 or 3, its a lot harder.
As far as the dog crate? You need solid dog house of sorts on one end. That would be the easiest solution. I would "wrap" the crate with hardware cloth.
I did something similar once upon a time, with a rabbit hutch.
I used J clips to attach the hardwire cloth to the wire. You could also use zip ties (and then cut off the "tails").
I would put corrugated PVC or that ondura roofing (lowes) over the crate to give shade. You may have to put a board inside the top of the crate and then screw the roofing down into that board, to hold it to the crate. The little cheap 1x2 boards would work fine for this.
If you don't want a separate dog house or solid walled enclosure attached, I would take plywood, cut to size (lowes or HD can cut for you OR they sell smaller sizes like 2'x2' or 2'x4') drill holes and then fasten to the crate with zip ties again OR do the same process as the roof. Put a 1x2 strip of wood on the inside and then screw the plywood from the outside into it. That would "sandwich" the metal wire between the plywood on the outside and strip of wood on the inside, holding it on.
You could cover one end with plywood. For example, if it was a 4 foot long crate, I would cover one end with plywood and then 2 feet of each side with plywood. Making a nice "nook" on that end.
I would make sure ALL corners are well protected as chicks tend to pile in corners, especially when scared.