that's really awful history, martin, I hope you continue to have strenght in this struggle. Some day your daughter will understand the terrible thing her mother did, and what you tried and are trying to do. Indeed, I read on some websites that the Hague should not be applied in your case, because the "habitual residence of your daughter was, in fact, in Brazil". Unfortunately, you have to continue the fight at the State Justice.
To avoid the payment of this guarantee, you have to demonstrate to the judge you have properties in Brazil, any documents you have about these properties should be shown to the judge. As it's a very serious situation (it can close your case), I recommed you first pay the guarantee and after you demonstrate your properties and recover the money, just to ensure your case is not going to be closed.