A girl wishes to marry a man who is already married. Her father refuses to give his consent, and has put so many strict conditions for him regarding her future life that the married man cannot possibly accept them. What does Islamic law say about:

a. A father opposing his daughter’s decision so vehemently.
b. A father refusing to allow his daughter to marry a man who is extremely pious, religious, educated, a high earner and one who is prepared to fulfil all Islamic conditions regarding justice and fairness.

It is the consensus of all jurists that to marry, a young virgin requires the consent of her father. Any conditions he sets are only to secure and protect his inexperienced daughter from an unknown future. Despite the proposed husband being pious, educated, and all the other things you mention, none of these rule out a father from speaking his mind. For her sake, he has every right to support and protect his daughter. This means that his consent is clearly needed in addition to that of the other parties involved. Indeed, he has every right to demand the approval of the first wife prior to his daughter marrying her husband.