How can I convince my sister to get breast reconstruction? She doesn't care.

Please don't try. Breast reconstruction is a very personal thing. She will do it when she's ready if she ever is. I always include doing nothing as part of my reconstruction options.
Agree with others. My colleagues have provided great answers. It is important to know that reconstruction can be done years later after treatment is complete. This option is always available and will still be covered by insurance. Please do not cause any more stress by imposing your ideas and wishes, although you mean well. She can wear a bra w/ prosthesis and feel great about her decision.
Just be supportive. Breast recontruction is a personal thing both in whether do to it and how to do it.. All you can do is support your sister as she is going through cancer treatment. Sometime just getting through the cancer treatment is all a patient can mentally handle. Good luck to your sister. Dr t.
You Can't. Inasmuch as I am certain you are trying to do what's best for her, you may be imposing your priorities rather than hers. This is a personal choice rather than a good:bad option. If you feel she is not making an informed decision, perhaps she will be willing to see a reconstructive surgeon with you, if only to reinforce her opinion.
Breast reconst. Good evening i perform 3 procedures a week, first you can not make that decision for her. That is her personal choice. The easiest approach is implants. Look under my gallery dr schnarrs on my website.