relentless that must have been such a difficult post to write.
I can't give you any reassurances. Sometimes we do our absolute best and sometimes even then we fall short.
What I do know is that you do love your daughter and that will help immensely.
Fwiw I think you're right that at some level your daughter will pick up on the rage within you. (she will also pick up on the love you have for her!).
I cautiously think you have to find ways to manage the areas where you know you are finding it difficult. Literally, consciously sit down and think out ways to handle times when you get mad or can't cope. I get the impression your little girl's father is around? can you sometimes ask him to take over? (everyone does this at times! but it may be even more helpful for you to be able to do it).
Counselling is an exceptionally good idea. If you can afford it, it would also be a good idea to see if you can find someone who gives child-rearing advice, maybe through the health visitor (they're called 'pedagogues' where I live but I'm not sure if there's a name for it in the uk).
I'd do it sooner rather than later because your daughter is still young and children don't half test your patience and your limits as they get older. They don't know when you have nothing left to give or are having a bad head day!. If you are able to get advice early it might avoid some of the nasty bumps that you can run headlong into without guidance.
Counselling is also a good idea as the sheer rage that you are feeling is hard to live with and is extra awkward when you have a little one. Even with the best will in the world, if you're containing anger and your little one does something naughty, it can spill over. (anyone who starts pointing fingers can butt out now. It's just human when you've come from a bad start. What matters is trying to handle it).
Also if you can, talk to your partner about how you are feeling. it can feel terribly dangerous but it's actually probably safer than bottling it all down.
A lot of people feel trapped by their children, if it's any help. Well, you -are- trapped. You've been your own person now there's someone who you have to put your own needs and pressures aside for. If it's any help it generally gets better over time especially when you have the will to do the best you can for your child.
A couple of links with people who have also struggled with their children, parenting in the front line:
[http://www.mumsnet.com/Talk/parenting/860205-I-need-to-find-somewhere-I-can-talk-openly-about?pg=1 I need to find somewhere I can talk openly]]
(Darn, I can't find the other one but the post was written by someone who was saying how hard they found it to have to do the endless round of utterly boring things like making dinner for them, wiping up, ironing etc. It was very honest).
Some people sail through parenting. You're 'supposed' to. But the reality is that many people don't and when you have a bloody awful example of parents yourself, you don't have a good model to draw on. But there -are- people who break the pattern of parenting. It's extremely hard work, but it does happen when they have the will to keep persevering and can keep on picking themselves up ... and it's not all grimness. There's the love back from your baby, and the good, happy moments.
Wishing you all luck, relentlessloss.