Rejection and Tolerance

I am seeing a girl and she says she likes me. I like her as well and we are planning to get engaged soon. Though we have not confessed whether we love each other or not, we have revealed our interests in each other and are waiting for parent's consent to proceed further. Unfortunately, both of our parents are quite fearful of moving ahead with this. I know for sure that my parents fear rejection and a blow on their self-esteem. And this feeling is getting on my head as well. If things were to go wrong from any side on this matter, it would weaken my spirit and dreams i have about life with this girl, to the extent that i may not be able to open up my heart for someone else
later. I have faced rejection in past and it proved nasty for my mental health and people in my family. Any advice on how do i proceed on this matter would be highly valued.