Difference between 与，和 and 跟?
I would reword the three sentences as follows instead:


她父母来我家与我家人见面。
她父母来我家和我家人见面。
她父母来我家跟我家人见面。


In this case, they can be used interchangeably as each one of them means "and".
Here are the minute differences:


与 [yǔ] is more elegant and formal, and is usually applied to similar items of abstract and contrasting nature. E.g. 天与地 (heaven and earth), 是与非 (yes and no).
和 [hé] is more general and informal, and can be applied to list dissimilar items and more often on objects. E.g. 汽车和现金 (car and cash), 蓝宝石和翡翠 (sapphire and jade).
跟 [gēn] is used more often in speech, and is usually applied to similar items and more often on humans. E.g. 他跟她 (he and she), 我跟你 (you and I).