Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If the parents have consented to the marriage, you should request them to delegate someone else as their wakil or representative.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
If the parents have consented to the marriage, you should request them to delegate someone else as their wakil or representative. Once they do so, you have no objection in taking the steps towards solemnizing the marriage. This is the best option.
Alternatively, you can also go ahead with the marriage if her parents unequivocally tell both of you in writing or in the presence of two witnesses that they would allow you to get married in their absence.
Almighty Allah knows best.