First of all, some questions for you:
(a) how many hours sleep is your DD getting overnight / in total over a 24 hours period?
(b) roughly, what is your daily routine with regard to waking up, feeds, etc.? I think that sort of detail might help more experienced mums offer you some advice.
In the meantime, I'm not an expert as I have only one DS, but I wanted you to know that you are not alone in stressing over the sleep/naps issue. My own DS struggled with being put down for daytime naps until he was weaned (at a controversial 20wks). Since then he will sleep mid morning and after lunch, for various durations (but usually 30-40mn in the morning and 1.5-2 hours after lunch). However, this is starting to change (he is now 9mths), and all the way through I've found that just when you are starting to despair, they get the knack of going down; and when you think that you have it licked, they want to change their pattern!
I couldn't stomach CC for daytime naps at all (my short attempts reduced both of us to tears around the 16 wk mark), although I guess we sort of got him used to a strict 7pm bedtime from 2 wks of age (partly from letting him cry for 10mn bouts, then comforting him, then putting him down; also not talking or making eye contact at night, dressing him in "day" and "night" clothes, and introducing a bath/boobs/bed routine from the outset).
As a breastfeeding mother, I have also at times succumbed to the temptation to "boob" him to sleep, although I do find that if I do that - and successfully transfer him from tit to cot, which is not always easy - he tends to wake up screaming 45mns later (during the 'light sleep' period of the sleep cycle). So, mostly I try to feed him, then say to him "Mummy wants you to go to sleep now. I'm going to put you in your cot," etc. And then I leave him to grizzle a bit. However, if he does any proper crying, I (or DH)usually go back for a cuddle and put him down again - I personally don't think my DS will go to sleep if he works himself up into a frenzy first).
As for daytime naps, do you put him down in a darkened room? Is there a bit of household noise? Some babies need dark and quiet during the day, others seem to want to nap with some light and background noise. Do you use a grobag for naps? Do you have a song that you use as a lullaby to "cue" your DD to sleep? It sounds a bit like your baby might be getting overtired/over stimulated before naps - could you spend 10mns quietly singing and cuddling before naptime?
Whatever all the books say, babies are all individuals, and if yours doesn't conform to any textbook pattern, so be it.
Finally, whatever advice you get here, and whatever happens, rest assured that things will get better.