Is it permissible to continue supplicating for marriage to a girl who has become engaged to another person, knowing that her current fiancé is not liked by some relatives?

It is impermissible to supplicate for a girl to be your wife if she is already engaged and both have settled with each other, as this involves striving to cause separation between them.

Do not grieve over what has passed, for there might be good in it that you do not know, as Allah the Almighty said: "No disaster strikes upon the earth or among yourselves except that it is in a register before We bring it into being - indeed that, for Allah, is easy - So that you may not grieve over what has escaped you nor exult [in pride] over what He has given you."

Resume your life and seek a righteous wife, seek Allah's help, strive for what benefits you, and do not say, "If only I had done such and such," but rather say, "Allah has decreed, and what He wills, He does."