I think that at 2 1/2 she won't be able to understand and that telling her now that Me-Ma is going to die would confuse and worry her.
I suggest that as your mother's cancer causes her to be ill that you tell your daughter that Me-Ma is sick just as you would if Me-Ma had the flu. If your daughter asks questions answer them as simply as possible. I could anticipate her asking why doesn't she get well? My answer might be because her lungs don't heal. She has a lung sickness. YOu could say cancer if she's hearing that word in relation to your mother. But she doesn't need to know that she's dying.
My granddaughter and I are also close. Several years ago I had a rare form of cancer that is unlikely to return. After one of my check ups I mentioned to my daughter that they saw a small spot and would be watching it They also said that it was most likely scar tissue. Later, they told me it had not grown and they were not concerned. Somehow my daughter kept thinking I once more had cancer. She told my 7 yo granddaughter that I had cancer and would die. She worried about my dying, kept asking me when I would die, etc. She acted angry with me. And then sometimes, too clingy. Finally she told me what her mother had told her. I immediately told them both that I was cancer free and highly unlikely to ever have cancer again because of the kind of cancer I had.
My granddaughter, since she was around 3, has been concerned about my being old and would I die? I talked with my therapist who said it was important for me to reassure my granddaughter that I would always be with her. As she got older we did talk about how old people do die and what that meant. I've told her that even tho I will die someday I will still always be with her in spirit. At 8 she is still confused about death and cancer. Her perception of time is still limited.
Your daughter is much younger than 8. I recommend that you tell her Me-Ma is sick when the cancer gets to the stage that she's unable to do the usual things with your daughter. I wouldn't mention dying at this early stage. As your mother becomes more ill you could talk about death in an abstract way. i.e. not as related to Me-Ma. When Me-Ma becomes very ill and near death is the time to talk with your daughter about Me-Ma dying and what that means.
Give information a little at a time as your daughter asks questions. Make your answers simple and appropriate to her ability to understand. I could understand that because of your own pain you feel it necessary to include your daughter in this process. Your daughter will pick up on your feelings. Be honest with her about how you feel. Just don't go into very much detail.
I just remembered that I had my cancer surgery when my granddaughter was near the age of your daughter. We told her I was going to have surgery, that I would be limited in what I could do afterwards. I wouldn't be able to pick her up. etc. She never asked why I was having surgery. She just accepted what we told her. She visited me in the hospital before and after surgery. At this age children understand very little about time and illness. Just saying one is sick satisfies them.
I empathize with you. The thought of losing a parent is very painful. Their is one advantage of knowing in advance that one's mother is ill and dying has a positive side. My mother and I talked about her death, how we both felt about it, shared thoughts, memories.
We grieved together, cried together, laughed together. We both believed in God and Heaven. My description of each is radically different than hers. Knowing she would be in Heaven was and still is comforting. I still feel her presence.
I sometimes talk to her.
If you believe in God I pray that His peace will be with you.
After reading other posts, I agree that it would be best to say Me-Ma has cancer rather than she is sick.