Having trouble laying eggs?

I haven't posted in awhile, but am thoroughly enjoying my girls.

But for the past couple of months, one of them, my "Silkie" (I'm sure she's crossed with something, she neither looks much like or acts like a Silkie) Ida has seemingly been having trouble with her eggs.

It started when she began laying for the first time 4 months after her same-aged buddy Nina - so she was probably 9-10 months old when she laid her first one. Then, after about a month of good laying she molted and went broody for a long time and didn't lay. Probably 2-3 months? Meanwhile Nina appears to have molted and never stopped laying. She has only missed a handful of days since she began.

Then Ida started laying normally again, about 4 or 5 eggs a week. And then after a month or two of that, the weird stuff began. At first I thought she was eating eggs because I'd find them broken and empty. Then I started finding them occasionally out in the middle of the yard, and apparently laid very late, like at dusk. Some looked normal, some were slightly misshapen, like with a flat side. Last night I went to close up the coop very late (10pm, well after dark) and found her sitting in the doorway of it. I let her finish, and when I went back out to check, she was back in the coop sleeping, and where she'd been squatting there were two eggs, one mostly normal, and one very thin shelled (rubbery, almost) and broken.

Sometimes she goes into the nesting box for a looooong time and finally lays. Sometimes she goes in for the long time, doesn't lay, and later I find her egg in the yard, like it just fell out of her when she wasn't expecting it. Sometimes she lays like a very normal chicken. The ones she has "trouble" with don't seem to be larger than her other ones. All the eggs taste normal and the ones that aren't broken have good, hard shells. When she doesn't lay for more than one day in a row, I'll often find one of these odd-egg situations on the third or fourth day and it happens in spurts, so that she goes a couple of weeks without a hitch.

She seems to be a content enough chicken otherwise, a little on the high strung side but she always has been that way. I'm just wondering if there's some supplement or something that she needs. I'd hate for her to get egg-bound or have an egg break inside of her, but that's what I worry about when I see what appears to be her trying to lay, not doing it, and then doing it later in random places.

They eat layer mash, scratch, and have free range of the backyard during the day. They have the option of oyster shell but don't seem to generally go for it. Lots of water available. Nina is the "boss" of the two, but there doesn't seem to be any conflict between the two (except tussling over tomato horn worms and things like that! )

Thanks for any explanations or suggestions you can give.