You're not a terrible mum and you're absolutely not a failure either.

And other mums may all seem to cope but you could bet on most of them having times/days when they don't cope or have tough days.

my two are a similar age gap to yours (2 yrs and 9 months between mine) and it really took me a while to find my groove. I actually stopped posting on bb because I felt like a rubbish mum. I'm not sure when things improved or whether I just chose to be kinder to myself. It certainly has got easier. Do you think some one on one time with your dd would help her behaviour at all? Stay consistent with her. If you google janet lansbury, her site had some great blogs and suggestions on dealing with behavior. Or she may be like my ds who just grew out of alot of it (at about 4.5).
Are there things you can do like online shopping to take some pressure off? Or taking your dd to a park so she can play and run off some energy. A good playgroup can be a great source of support (and sanity!) too.
be gentle with yourself and give yourself time to adjust. You're not damaging them but you do need time to nourish yourself