Whatever you do make sure that your daughter knows you are still there for her and love her. Me and my partner had the same problem a few months ago and it still happens occasionally,when ex hasa bee in her bonnet about something he sometimes doesn't get to speak to his daughter for 3 wks or more, the first time she stopped him from seeing her and he threatened to take her to court to get proper access sorted out and she relented. Your ex, like my partners is using your daughter to punish you as you say, she may even be telling your daughter you don't want to talk to her,etc. When we went through this we made sure my partner sent her a card and a letter every wk, even sending her a writing set with the envelopes pre addressed and stamped so she could write back and just post it herself if she wanted. We used recorded delivery so we could track the card and make sure it had been delivered so she couldn't make out that nothing had been sent and kept the stubs to show his daughter when he did finally see her to prove that if she hadn't received anything at least she could she he had been trying to keep contact.
Don't give up, she is obviously a very selfish woman who cares about getting you upset rather than letting her daughter have the stability she needs, as other people have said-consult the CAB or a solicitor and if you don't have parental responsibility then look into it and apply for it, then she will have to think twice about emotionally blackmailing you!!
Good luck! :o)