All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Your fiancé does not become unlawful for you in marriage merely because of the feelings you have when touching the hand of her mother.
If the mother is one of your non-Mahram (marriageable) women, it is impermissible to shake hands or touch her, even without lust. It was narrated on the authority of Ma‘qil ibn Yasar that the Prophet said: “If one of you were to be stabbed in the head with an iron needle, it would be better for him than touching a woman whom he is not permitted to touch.” [At-Tabrani]
You should beware of doing whatever may lead to Fitnah (temptations) and falling into sin with her before or after concluding the marriage contract.
Allah knows best.