Yes, your mother can gift her self-acquired property to her grandson because she is the absolute owner. There is no legal bar in transfer of that property through a deed of gift.
That property is existing at the time of making the gift, the donor is authorised to transfer that property and donee is also competent to accept the gift. Hence, all the legal requirements for a valid gift deed have been fulfilled.
You cannot stop your mother from executing a gift deed. If she is competent to give free consent and a lady of sound mind she can execute a gift deed.