What was Andromeda Tonks's relationship like with her sisters before she was disowned?

There's very little information in the Harry Potter books and films about the early life of Andromeda Tonks (née Black) other than a few quotes and some basic assumptions we can make;

The main quotes come from "The Order of the Phoenix" and "Half Blood Prince"

"‘Oh, yeah, her mother Andromeda was my favourite cousin,’ said Sirius, examining the tapestry carefully. ‘No, Andromeda’s not on here either, look –’ He pointed to another small round burn mark between two names, Bellatrix and Narcissa. ‘Andromeda’s sisters are still here because they made lovely, respectable pure-blood marriages, but Andromeda married a Muggle-born, Ted Tonks, so –’ Sirius mimed blasting the tapestry with a wand and laughed sourly."

and

"‘She is no niece of ours, my Lord,’ she cried over the outpouring of mirth. ‘We – Narcissa and I – have never set eyes on our sister since she married the Mudblood. This brat has nothing to do with either of us, nor any beast she marries.’"

Per the description in the Harry Potter wikia; I think we can reasonably assume that her relationship with her two sisters; Bellatrix Lestrange and Narcissa Malfoy was always precarious

• Both Bellatrix and Narcissa are both "pure-blood" fanatics whereas Andromeda was open to the idea of having a relationship with the muggle-born ("mudblood") Ted Tonks

• She was apparently Sirius' "favourite cousin" despite the age difference between them (6-8 years) so again, we can assume that they shared similar views.

• When she married Ted, she was immediately disowned by her sisters, neither of whom ever spoke to her again. Hardly the action of a loving family

• Let's not beat about the bush here, Bellatrix is a sadist and a psychopath, mentally unhinged and possessed of a volcanic temper. Growing up with her must have been very challenging even with magic to defend you.

As I said, all of the above is little more than supposition + intelligent guesswork. Whether JKR will at some point add some extra info on Pottermore (and whether Narcissa ever reconciled with Andromeda) remains to be seen.

I would say that Andromeda´s relationship with her sister Bellatrix must have been strained from the beginning due to Bella´s "eruptive" temper, and somewhat tainted with her younger sister Narcissa because of the latter sister possibly being judgmental and maybe influenced by Bellatrix.