I honestly think it depends on just how premmie your baby is as well. They say that your baby's development is taken from their corrected age and that they catch up fully in size etc by the time they are 3-4 years old.
My little girls was 11 weeks prem and to me she is 'normal'... I have accepted the fact that along with your introduction to new people your friends always add and this baby is a prem, or when people ask how old she is and I say 4 months their faces drop like I am starving her because she is still small so I end up reluctantly adding that she was premmie.
As far as I am concerned if your baby is past their due date (which your baby is) and is a good size now on their chart then treat them like a 'normal' baby. I have done this and my little girl has responded beautifully. ALL babies can get over stimulated but your baby will tell you that by getting agitated.
It is very frustrating I know and you feel like you are always carrying this big sign that says "YES THIS BABY IS A PREMMIE" and everyone gets sympathetic. It is important to explain to your friends and family that you do not want sympathy (unless you do of course), your baby IS NORMAL and you would like them treated that way and most importantly for me has been to make sure that you treat them as a full term baby once they are big enough and strong enough to be treated that way. Eventually people will pick up on the fact that if you treat your baby as you would a full term baby that they should as well.
If you do want people to be more sensitive to the fact that your baby is a premmie there is a heap of literature that you can get hold of that helps to explain the differences of a premmie. Go to your library and borrow a few books and it might help your mum to understand a bit more. Some major hospitals also have library services or you could try your local university library as well (or the net).
ALL babies respond differently to everything and all develop at different rates, whether they are prem or not.
I hope that helps!
WA, Baby Girl (Tayah) born June 04