How can a Muslim woman forget her love for a married man who promised to marry her but did not, even though she knows this love is impermissible, despite her many attempts to do so?

What you have fallen into is ardent love, which is a dangerous ailment. Ibn al-Qayyim mentioned guidelines for its cure in Zad al-Ma'ad. You must supplicate to Allah and sincerely seek refuge in Him. If you do so with sincere resolve, you will be saved, as Allah Almighty says: ﴿And when the matter is determined – if they had been true to Allah, it would have been better for them.﴾ [Muhammad:21], and as the Prophet, peace and blessings be upon him, said: «If you are true to Allah, He will be true to you.» His marriage to you might not be good for you, especially since he already has a wife, and many marriages based on love fail. Entrust your affair to Allah and ask Him to facilitate a righteous husband for you, for that is better for you. Allah Almighty says: ﴿But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows while you know not.﴾ [Al-Baqarah:216]. Al-Tahir ibn 'Ashur indicated that the verse calls for a deeper consideration of the consequences of matters and not to be deceived by outward appearances or by the inclination of desires.