"El valor del respeto" refers to respect as a family value.
And "venir de familia" is, as Rusty said, talks about something that is an inherent characteristic of a family.
The author is saying that respect is a value spontaneously or even joyfully instilled in her family. Maybe, as Rusty said, is something that might apply to her family only, but many people are convinced that virtues and principles by which people live all start as positive and strong family values.
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