Is a girl afflicted with cancer sinful if she accepts a second legitimate marriage from a married man, knowing that polygamy is not permitted in her country, and is this considered a betrayal of the first wife, and does her father have the right to refuse on account of the first wife?

You bear no sin for a lawful marriage as a second wife, even if your country prohibits polygyny, because this prohibition contravenes Islamic law. As for your father preventing the marriage, if it is solely because the man is already married, then he has no right to do so. However, if the prohibition is due to harm that would befall you, then he has the right, and in that case, he would not be considered an oppressor ('aadil). You should try to reason with him or ask someone to mediate on your behalf. If he agrees, then all is well. If he refuses, then obey him, unless there is harm in your not marrying. In that case, refer your matter to the judge.