Should I give up?

[ToiletTraining]

Have been potty training DD (2.9) for the last two months. Initially it went well (thanks to chocolate bribery) but she never pooed on potty/toilet just pees. She either poos in her pants or even she has a nappy on for her nap. My issue is that she won't go voluntarily to the toilet. She can hang on for ages and will pee in the potty/toilet if I put her sitting on it but if I leave her, like this morning, she will just pee in her pants no matter how much I remind her. She definitely knows when she needs to pee or poo.
I am so sleep deprived from DC2 that I feel really angry with her when she does it. Which I am crap at hiding and feel shit about.
I think I need to give up?
I am ashamed to say that I am hesitating because I am so embarrassed. Nursery will probably think I'm wrong as she doesn't have accidents there (again doesn't take herself off to toilet but isn't there long enough to have accidents), all the other kids her age are trained. Her cousins the same age are all trained. My kids just seem to always be last with everything.
I know I shouldn't care and I am ashamed of myself for thinking like this but I am embarrassed.
But if she doesn't want to go to the toilet in wasting my time aren't I?

[mumatwork999]

I think I would get her back in nappies/pull-ups to take the pressure off you both. My DS is only just going to the potty for wees and he is 3.5. He knows when he needs a wee and a poo and is often dry in the mornings but is a bit willful and I've just had to let him do it in his own time. There are still other 3YO at his nursery in nappies so even if it seems late in terms of your experience it really isn't. Nursery of course will want kids out of nappies as soon as, as its easier for them, but you need to do what fits in with you and your family, not them!