Is it permissible to complete a marriage with a girl who was engaged to someone else, and I helped her break off that engagement after her family refused him, and what is the expiation for that if it was a sin, and is the current marriage’s difficulty an indication of that sin?

It is forbidden to propose to a Muslim woman who has already been proposed to by another Muslim, except in specific cases, such as the fiancée rejecting the first suitor, or the first suitor agreeing to another's proposal, or if the first suitor grants permission, or if the second suitor is unaware of the first suitor's acceptance. If the fiancée rejects the first suitor, even if her guardian has agreed, the ruling of acceptance is nullified because the right belongs to her. If you propose to her after knowing of her rejection of the first suitor, there is no blame upon you. Delays in marriage may be a trial, not a punishment, and it is advisable to supplicate and avoid excessive dowries, while noting that speaking to a non-mahram woman is not permissible except out of necessity and with adherence to Islamic guidelines.