What is your guidance to a woman who prayed to her Lord for a righteous husband, then married someone in whom she discovered many despicable acts and lies, and her religious devotion and marital life were negatively affected, and she is unable to divorce, and do you support her resorting to in-vitro fertilization?

If the situation is as you described, then do not seek to have children with this man, and you must separate from him through divorce or khul'. Let not your family's circumstances deter you. For no matter the harms of separation, they do not compare to the harm of remaining with him in that state. If you are keen on pleasing Allah and rely on Him, He will provide for you and suffice you concerning what worries you. Allah Almighty says: (And whoever fears Allah - He will make for him a way out And will provide for him from where he does not expect. And whoever relies upon Allah - then He is sufficient for him.) And Allah Almighty says: (But if they separate [by divorce], Allah will enrich each of them from His abundance.) So, divorce can be a blessing that removes the shackles from the neck and the fetters from the leg.