my dad has some health issues.
mum is fine.
mum will go with dad to the GP. There are various reasons for this.
Now... in relation to mental health, it took myself (and mum?) about a year to convince dad to speak with a professional about mental help. At this time, I was also seeing them once a week because of my own situation.
On the advice... what you said here can said to your mum... I dont have all the answers or I dont know.
But you can still listen.
And you can say "that must be " which is perfectly OK.
If it requires a visit to a GP can someone make the the appoint to go with her? There is a difference between denial of a problem and not following through.
I also think from your post you care very much about your mum and to say something like "I care very much about you and would like to spend more time ... and this is hard on you ... and to do this maybe having a chat with your GP would be helpful. What do you think"
PS. Beyond blue also has pages on supporting some which might be worth reading as well.