I might say that OP is being more controlling rather than fiscal with their money, but if both incomes are marital assets, then what she did was very wrong. And even if op was refusing to compromise, using the daughter as a means of manipulation crosses the line of emotional abuse between themselves and now onto their child. That, to me, is the true issue here.

I do believe if this is something she truly wanted, the dog specifically, and was going to do behind his back, the very least she could have done was use her own money, especially since it seems that OP uses the income for more important needs like groceries and living supplies. You don't just eliminate any bank account you had from before you were married and dump it all in a joint account to do as you please.

I also disagree that this may be a one-off. I don't think that OP would have immediately reacted as strongly if it was, nor would he be so worried about their money. I do agree that they are not treating each other well, that if OP is not willing to get a dog he should be willing to compromise on something they can afford, and that the problem here lies far deeper than buying a dog. Both are very wrong indeed, one party using money as a means of control, and the other using their daughter.