You say the bad news was from your mammogram. Usually a mammogram indicates only that there is an anomaly which needs more tests to discover whether what is revealed is a malignant tumour, a benign tumour which won't spread, a cyst, or just a technical glitch. When something was found on my mammogram, it took a second mammogram and an ultrasound scan to show the tumour, and a biopsy to prove that it was indeed a malignant cancer.
Have you had these other tests, or are you assuming the worst from one mammogram? And how do you know at this early stage that you will need chemotherapy - that is usually only ascertained after the primary tumour has been removed and examined in the laboratory.
If you have a definite diagnosis of a malignant tumour, and have been told that you will have chemotherapy, then you have my sympathy. It is not an easy journey - but it is better than the alternative of just letting it kill you slowly.
If you are using the evidence of one mammogram to hurt your daughter, then that is indeed emotional blackmail, and as has said before is not fair. Only you know whether you doing this.