There is at least one part of the question that is wrong - that Maria was of "proper education". This is, in fact, one of the main morals of the story - the education of Maria and Julia was actually seriously mishandled.
While Sir Thomas Bertram has (according to the novel) a sound moral understanding and a willingness to pass this on to his offspring, he is ineffectual in doing so, while having his efforts undermined by Mrs Norris (Mrs Bertrand is so indolent as to not be a significant factor - we are told in Chapter II that she "paid not the smallest attention" to the education of her daughters). Had Sir Thomas taken a evn closer interest in his children, and been a slightly less dreadful character to them, he might have detected that Maria (and, to a lesser degree, Julia) were in fact morally defective: both sisters were perfectly able to show good manners and a presentable front as long as the stakes were low, but when they were put in a situation that required good moral fibre, they failed. This is pretty much all put explicitly forward in Chapter XLVIII.
Maria's actions are actually easy to understand: she is married to a dull but rich man, whom she has nothing very much in common with and whom she does not care for. She is morally very shallow and her reputation is at best a secondary concern. Recall the whole play episode, where being close to Henry Crawford is so important for both her and Julia that they are willing to go to great lengths, even at the risk of making a scandal. Maria might have either not given the consequences of an affair with Henry much thought, or she might have believed that she could easily keep it secret.
As for Henry, well, I do not think the explanation we are given in Chapter XLVIII at all unlikely: essentially they met, Maria was cold and indifferent, and he decided that he wanted to see her foolishly in love with him again. His love for Fanny, we are told, only spurred him on: he wanted to see Maria humiliated in order to elevate Fanny. He might have rationally understood that this was an unwise action, but as he never was trained to restraint, such understanding did him no good.
Ultimately, a lot of energy in the book is spent on presenting the Crawfords as morally corrupt, and Maria as without strong moral backbone. Neither of them are used to considering anything but their own pleasure or the direct risk of getting punished. Without more strict moral training than that, neither can resist the chance for quick gratification.