A google search came up with a few different configurations for the price of a french drain. Deep-trench drains of significant length could be between $6k-10k. The average shallow french drain between 30 and 50 feet long, would be between $350 and $1500 but average just under $1000.
I get that this is something that this definitely needs to be dealt with, and that you'll probably need to seek recourse from the courts. But you also need to ask yourself which is more urgent: fighting a lawsuit, or preventing more damage to your property.
Both sound like they're necessary. But if one waits too long, the other might be devastating.
What I would do is what was addressed already up-thread I think: put your concern and request in writing, in plain English. And mail it to your neighbor, return receipt requested. That way you have proof that a) you knew it was a problem and b) you tried to get her to fix it, at such and such a date.
Otherwise she could just say "what problem? I didn't know there was a problem." You need proof that she knows, if you intend to bring it up in court. Whether it's a problem caused by her, or by whoever put the pipes in, or by the sewer company, or whatever else - that's all research that needs to be done before you take it to court.
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