It means relationships of any sort. My interpretation was "She has two [romantic] relationships," which I think most people would jump to out of context. In specific contexts, however, it might mean that she has two familial connections. It's hard for me to think of a context in which it might take this meaning, though. Maybe, "Mit unserer Familie hat Sabine zwei Beziehungen." (With our family, Sabine has two connections). Maybe Sabine is married to your brother and Sabine's brother married your second cousin?
But yeah, out of context I just took it to mean that she's dating two people at once (though the relationships are not necessarily sexual).
If you can gargle, you can pronounce the german "r" - it's a similar throat movement. Kinda sounds like a cat purring. It took me a long time to figure it out, but I got there eventually. Walked around Berlin like an idiot repeating "warum" haha. Just have to practice. Hard to tell when listening though.