Hello Evelyn – greetings to Kualalumpur!
let me paraphrase your question to make sure I understand: you have a client who is over 60 years old and who is pushing herself harder than you recommend. You believe that she is over-training.
Ultimately, you are the best judge of that because you can see her for yourself. There are some indications that over-training is the case when a person continues to exercise despite injuries, shows fatigue, may be more prone to colds and seems to show signs that previous fitness gains are diminishing (which in turn prompts her to try even harder and creates a vicious cycle).
If you notice any of those signs, you may try to explain to her what she is doing in hopes that she will give herself the rest she needs.
This can become a very difficult situation because you do not want her to get hurt but at the same time you do not want to be associated with her non-compliance. Your reputation as a trainer is at stake.