. . . and her car brakes failed
Sorry, but this always makes me chuckle. As a P&C guy, I hear this a lot. Face it, more than likely, it was a simple 'oops'. No big deal. As long as nobody is hurt, everything else is fixable.
For the most part, claims follow a very orderly process on who pays for what. This is straightforward, not something that is really open for debate either.
If you could file the claim against your homeowners, you would be responsible to cover your home deductible (probably more than the repairs) and if the carrier paid, you're homeowners rates will go up. If the carrier subrogates back to the auto company (and they would), then you would get reimbursed for your deductible, your rates probably would not be impacted, but hers would be.
Here is where a good agent can help. You need to know the rules for rated accidents in the state you are in. It is going to depend on the dollar amount of the damage.
Dan