Praise be to Allah.
Salaat al-istikhaarah is a confirmed sunnah that is proven in reports from the Prophet (blessings and peace of Allah be upon him), and it cannot be replaced by what you have mentioned about seeking auspicious omens in the Qur’an. Rather these seeking omens in the mushaf are haraam according to a number of scholars, because it comes under the same heading as divination with arrows.
Al-Qarraafi (may Allah have mercy on him) said: With regard to the haraam pursuit of auspicious omens, at-Tartooshi said in his commentary that looking for auspicious omens in the Mushaf, geomancy, drawing lots, throwing grains of barley (and interpreting the patterns in which they fall), and all such things are haraam, because they come under the same heading as divination with arrows. During the Jaahiliyyah, they had arrows or pieces of wood, on one of which was written “Do it”; on other arrows were written the words “Do not do it” and “Not clear (or try again)”. A person would draw one of them, and if he found the words “Do it” he would go ahead with what he was thinking of doing; if he found the words “Do not do it”, he would turn away from what he wanted to do and think that it was bad; if he found the word “Not clear (or try again),” he would try again. Thus he was seeking his share of the unseen by means of these arrows, so that if it was good he would pursue it and if it was bad he would forget about it. The same applies to one who looks for auspicious omens in the mushaf or elsewhere; the one who does that thinks that if he sees something good he will pursue it or if he sees something bad he will try to avoid it. This is exactly what is meant by divination with arrows which the Qur’an states is haraam. (End quote from al-Furooq, 4/240)
Al-Nafraawi said: The Prophet (blessings and peace of Allah be upon him) liked good omens, which refers to anything that makes one feel at ease, such as a good word. In as-Saheeh it says, “There is no tiyarah (superstitious belief in bad omens), and the best of it is a good omen.” It was said: O Messenger of Allah, what is a good omen? He said, “A good word that one of you hears.” According to another report, he said, “But I like good omens.” An example of that is if a person sets out on a journey or to go and visit a sick person and he hears the words Yaa saalim (O safe one), yaa ghaanim (O winner) or yaa ‘aafiyah (O healthy one). This applies if he was not seeking such an omen (and heard that by coincidence); but if he was seeking an omen so that he could act upon whatever he heard, whether it was good or bad, then it is not permissible, because it is like the haraam divination with arrows that they used to do during the Jaahiliyyah. A similar practice, which is also not permissible, is looking for omens in the mushaf, because this also comes under the same heading as divination with arrows, because he may find something in the Qur’an that appears to point to something he does not like, and that may lead him to regard the Qur’an as “unlucky”. If a person wants to do something then hears something that upsets him, he should not change his plans; rather he should say, “O Allah, no one brings good except You and no one brings evil or wards off evil except You.” (End quote from al-Fawaakih ad-Dawaani, 2/342)
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked about looking for good omens in the mushaf. He replied: With regard to looking for good omens in the Mushaf, there is no report of that from the early generations, and the later generations disputed concerning it. Al-Qaadi Abu Ya‘la mentioned a dispute concerning it. He narrated from Ibn Battah that he did it and said that someone else disliked it. But this is not the kind of good omen that the Messenger of Allah (blessings and peace of Allah be upon him) liked; he liked good omens and disliked superstitious belief in bad omens. The kind of good omen that he liked is when a person does something or decides to do something, putting his trust in Allah, then he hears a good word that makes him happy, such as if he hears the words yaa najeeh (O successful one), yaa muflih (O prosperous one), yaa sa‘eed (O happy one), yaa mansoor (O victorious one) and so on. For example, during his hijrah (migration to Madinah) he met a man en route and said to him, “What is your name?” He said: Yazeed (meaning increase). He said, “O Abu Bakr, yazeed amruna (our matter will increase in good).” As for superstitious belief in bad omens, if a person has done something, putting his trust in Allah, or he has decided to do something, then he hears a word that he dislikes, such as “It will not reach its goal” or “He will not prosper” and so on, and he takes it as a bad omen and gives up his plans, this is forbidden. It is narrated in as-Saheeh that Mu‘aawiyah ibn al-Hakam as-Sulami said: I said: O Messenger of Allah, among us are some people who superstitiously believe in bad omens. He said, “That is something that one of you feels in his heart; do not let it prevent you from going ahead.” Thus the Prophet (blessings and peace of Allah be upon him) forbade letting superstition prevent one from doing what one intended to do. In both cases, even though he liked good omens and disliked superstitious belief in bad omens, he would still pray istikhaarah (seeking Allah’s help in making a decision), put his trust in Allah and go ahead on the basis of what is prescribed of taking appropriate measures. In the case of a good omen, he did not make it a reason or motive for going ahead, and he did not let a bad omen prevent him from going ahead. Rather it was the people of the Jaahiliyyah who based their decision whether to go ahead or not on that, for which they would use arrows for divination. Allah forbade using arrows for divination in two verses of the Qur’an; when they (the people of the Jaahiliyyah) wanted to make a decision, they would bring sticks like arrows or pebbles or something else on which they had made marks to indicate “good”, “bad” or “unclear (or try again).” If they picked up the one that said “good,” they would go ahead with their plans; if they picked up the one that said “bad”, they would refrain; and if they picked up the one that said “unclear”, they would try again. And there are other actions that could come under the same heading, such as throwing pebbles or barley grains (and “reading” the patterns in which they fall), or using boards, pieces of wood or pieces of paper on which were written Arabic letters, verses of poetry and the like, by means of which a person would decide whether to go ahead with his plans or not. All of these are forbidden because they come under the same heading as seeking divination with arrows. Rather it is sunnah to pray istikhaarah, seeking guidance from the Creator, and to consult other people and find out on the basis of shar‘i evidence what Allah likes and is pleased with and what He dislikes and forbids. These superstitious practices are sometimes intended to find out whether what a person wants to do is good or bad, and sometimes they are intended to find out about its usefulness, in the past or in the future. In either case it is not allowed or prescribed. And Allah, may He be glorified and exalted, knows best. (End quote from Majmoo‘ al-Fataawa, 23/66)
Thus it is clear that seeking good omens from the mushaf by opening it and looking at the page, then basing one’s decision on that, is haraam and is the same as seeking divination with arrows. This is in contrast to good omens that come immediately after one has taken a decision, when hearing a good word by coincidence, when not looking for that.
What is mentioned in the question about the wife who is not being given her rights by her husband indicates that the method mentioned is not correct, because one may say: Rather the verse mentioned indicates that she should separate from him and stay away, even if she fears the consequences thereof, as the mother of Moosa threw her son into the river, but the consequences were good for her.
In such cases it is essential to examine the problem and its causes and ways of dealing with it in the appropriate shar‘i manner, such as offering sincere advice, and looking for arbitrators from the husband’s family and the wife’s family, and so on.
And Allah knows best.