This thread illustrates why I’ve been increasingly less interested in engaging with Mumsnet over the years. Gone is the cameraderie, support and humour that, many years ago now, used be offered as advice, to be replaced instead with a petty, self-righteous and judgemental pile-on. What, are you all such wonderful, perfect parents that you feel morally superior enough to come down so hard on the OP, even when she has made it clear the responses have seriously upset her? 
To be honest, many posters sound as morally developed as Year 8 kids... so much so that at one point I wondered whether OP’s daughter had her school friends respond to make her mother feel (unnecessarily) guilty.
SqueamishMum, I feel I’m reading a different opening post to the one everyone else read. To me, the t-shirt and what it looks like is a bit of a red-herring that everyone has become ridiculously fixated on. I read that you gave your daughter money to buy some clothes and she responded by disrespecting you. You did not ask her to return the t-shirt because you didn’t like it, the post shows that you were responding to her behaviour.
And indeed, her behaviour was rude and contemptuous. I feel your first instinct - to ‘just parent’ - was right. There are lots of ways you might have gone about this - reminding her that you are far less likely to take her shopping or hand her over your hard earned cash in future, if this is the way she responds, is one option. You might have chosen to confiscate all her purchases until she apologised for her behaviour. You might have sat her down and had a very serious discussion about reciprocal respect and your expectations of her behaviour when you trust her to have the maturity to spend money you hand to her. Making her return the t-shirt is another option - maybe the lesson here is that this particular parenting option made it all about the t-shirt and not the real issue - her behaviour towards you.
You have disclosed some information about your difficult relationship with your ex. I am really sorry to hear this. 
It sounds to me like you have a history of being belittled and undermined. I hope you know that you don’t deserve to be belittled in this way, not by your ex, not by your daughter, and not by posters on an Internet forum. You sound like a great mum and an individual who is far more open to challenge and self-learning that the majority of the population.
I would be concerned that the damage done to you by your ex is now making you second guess your parenting decisions. Furthermore, there is more than a hint that his attitude towards you is allowing your daughter to feel she can also disrespect you. That’s not right. For her sake and yours, she needs to understand that it is not ok whenever he badmouths you to her. With patience, you can get this message across to her without it sounding like a personal attack on her dad. It’s not ok for her father to speak to or about her mother like that, in the same way it is not ok for her future partners to speak to her or about her like that.
You are right to draw the line at the disrespectful and demeaning behaviour your daughter showed you. Posters have focussed on your response in the shop, saying that it was humiliating to her. I see very little evidence that she was in any way humiliated - she cheerfully went back shopping and indeed smugly left the shop with her t-shirt safely in her bag. There is absolutely no sign whatsoever of teenage angst or trauma. She went about her merry way, doing exactly as she pleased.
Indeed, thanks to the pile on (and I’d love to see how wonderful their children really are!!), you even apologised to her. Has she shown any awareness of - not to mind remorse for - the way that she behaved towards you?
Your daughter has her ugly t-shirt now. She can wear it to make a statement about who she is, however crass or cringeworthy you might find that. That’s not what’s going to damage her, but not learning to be considerate very likely will.
You can still set ground rules to help her understand that you are worthy of and expect her respect. For example, you might decide to say you will confiscate the t-shirt if she wears it to the playground in case it upsets little kids (she needs to learn to consider how her decisions will impact others). Or that if she is contemptuous of you in public like that again, there will be a specific consequence.
She will also learn when you reward good behaviour - sometimes for a 14 year old, just telling them “I was really proud when you...” is enough of a reward.
Good parenting is not easy and putting your teenager on a pedestal and giving them a carte blanche for all behaviour other than taking drugs and physical abuse is not good parenting. Teenagers, especially young teenagers, need boundaries to feel safe and they need room to make mistakes so they can learn. They literally do not have the brain processing skills they (or most of them! 
) will develop as they get older for consistent effective decision-making.
Finding the balance between these, often conflicting, teenage development issues is something almost all parents struggle with (no matter what they say!). Please don’t beat yourself up for being a normal parent. For what it’s worth, I think your parenting instincts are probably stronger than most.
Look after yourself SqeamishMum and please don’t let yourself feel cowed or browbeaten by a bunch of catty strangers on an Internet forum. You absolutely deserve the respect you are seeking.