What is the ruling on the action of the girl's father in dealing with two young men who proposed to his daughter at the same time, and is the suitor sinful for breaking off the engagement due to his feeling of betrayal by the girl's father?

It appears that the girl was not inclined towards the first suitor. The father's request for you to visit them to propose to his daughter before the first suitor is accepted is not considered "proposing over another's proposal," which is forbidden, because the prohibition applies only if the woman has agreed to the first suitor. Fatima bint Qais (may Allah be pleased with her) mentioned to the Messenger of Allah (peace be blessings of Allah be upon him) that two men had proposed to her, and she had not agreed to either of them. If the girl is righteous, we advise you to proceed with proposing to her.