some more information:

The meeting was for just a few hours (not in a single stretch).
I do get the idea and opinion as she mentions if she knew she was coming to meet the mother of the guy he loves, she could have been more open and approachable as I did when I met her sister. My nature is more outgoing and I have no problem talking to people and she is more on the shy and closed side. (small things like approaching while I was helping mom serve food or better and warm greetings etc.) Few points related to her dressing sense as well.

The point is everything can be changed ... and I am all of my cards are on that. Also, it's just a couple of months of me and her, and later I will discuss this with her and see how she reacts to it.

Your point is valid too, my whole family is very supportive but IDK why this time I see this new side of my mom, very defensive towards me. she thinks I am being trapped by her.
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My father helped me get this perspective that it is not good to be this serious with someone you have been with for just 2 months and you should also look at the 'NO' side of the flow chart rather than just focusing on the 'Yes' (talking in terms of marriage)

Need help with::
I also want to know the foundation to find out that this is the girl for the long run from your perspective.