I get what u mean about the second day hair. I tend to wash my hair a lot bc by the second day it is a disaster so the answer seems to be to wash it. But honestly try washing your hair like korkscrew said, maybe twice a week or so.
Do you wrap your hair at night? Or do you at least put it in a pony tail so it isn't rustling around the pillow as u sleep? If so, you should try wrapping your hair with a silk scarf, or using a larger pony tail, so it doesn't rip hair, and put a big poof of your hair at the top when u go to sleep. This can help for 2nd day hair so its more manageable.
Unfortunately, I am still learning how to do second day hair myself, but I noticed a lot of women on here, just use a leave in to sort of refresh the curls. Also, you can try a lavender spray which is supposed to refresh the curls. Search the stuff on here to what is affordable, etc.
I do not know what brands that make specifically only coconut oil; however, the shea moisture curling souffle, is sold at walmart, target. I think they are now 10.99 but check bc they were for a while, 9.99. This is the closest for now that I can get to coconut oil since it is a predominant ingredient in it.
Lastly, I think the type of conditioner that you use as a co wash is vital. I noticed that the cheaper, more watered down conditioners I was using, made my hair bad on 2nd hair days. The more thick and better ingredient conditioners actually left my hair nice on 2nd hair days. So, assess your conditioner and see if maybe that could use a change. And concerning the wide tooth comb, do you comb your hair even after co washing? Once I got out of the shower, I used to put a little leave in and then comb again, and it made my hair worse. Now, even though it bothers me bc I see frizz and my first action is to run to the comb, but I am now only combing when I co wash and after that i leave my hair alone and simply use my fingers. Bc your hair is so fragile especially when nothing is protecting the hair shaft, so a finger is a lot more gentle.