How to explain what Buddhism is? My mother and I come from a non-Buddhist culture/background/society/country/family.

At one point when I had an opportunity to explain to her what Buddhism is, I was doing well (i.e. she was listening and accepting what I was saying) when I was explaining that Buddhism includes a non-fixed identity-view and explaining why a non-fixed identity view is skillful (e.g. because an attitude such as attachment to your job/profession might be unpleasant when you retire, and because people's abilities and health change with age).

But then what I mentioned the first Noble Truth she seemed to object, saying "Sorry you think life is suffering/dissatisfaction, I don't agree: I like life, I think life is good."



So


Do you ever try to explain Buddhism to someone who barely knows the first thing about it, and if so what is your strategy for how to explain it?
Do you explain 'dukkha' using the classic 'death/poverty/illness/old age', and/or is there a better way to explain the first noble Truth?
Are there any alternate way to introduce Buddhism which don't begin with the first Noble Truth?
Might it be better to explain what I think Buddhism might mean to me (why it appeals to me) personally? I fear that might make it less strange to her ("yes I see why you like it") but at the same time less acceptable ("but it isn't for me because I'm not like you").
Should I understand that if that's her reaction it's because she's already doing a lot of things right (e.g. not spending her life feeling angry)?
In a nut shell Buddhism revolves around the 3 trainings:


Living a life of morality so we do no create misery for one self and others
Developing mastery over the mind so we do not react but be proactive so we can be at peace with our selves and other
Developing wisdom of your cognitive process to identify how misery is generated so we can come out of misery