This is an EXCELLENT question.

My first headcanon for Viney's family is that she grew as an orphan kid, and she was raised mostly by uncles and cousins who lived deep in the forests or far from the most populated areas of the Islands, which is why the idea of ​​combining magic wasn't so crazy for her, because her family raised her under the teaching of wild magic and a bond with nature and it is easy for her to understand the concept of communities and found families. I like to picture Viney's childhood as a kid who was educated at home until the adults had no longer more things to teach her or her curiosity started to grow bigger than their knowledge, so she ended up attending Hexside (the closest public school lol). Her family also lets her go with puddles bc sure why not take your half-ton pet to school babygirl she can take care of you.

Her being a home-schooled orphan is a major point for my headcanon because of her adaptation issues at Hexside and the massive concept of loyalty she has. In distant communities you have to support each other to survive and coexist in harmony, so betrayal or dishonesty are a deal breaking for her, and she appreciates actions over words.

So yes I picture her family to be her whole community of uncles and distant cousins who live in the woods and practice freely any kind of magic, although more focused in healing, beast-keeping, plants and potions (even construction, they must be buff and STROONG).

PS: i hope you can see how i am implying a massive counterpoint in her relationship with emira wink wink.
PS2: I can't no longer say excellent without thinking in p&p mr. collins 'excelent boiled potatoes'.