I am so sorry you and your mum are having this worry at the moment. When the biopsy has been performed, the tissue removed is tested in the path lab with oestrogen/progestogen and HER2 (the human epidermal growth hormone). If it is positive for HER2, it simply means she will need Herceptin as part of her treatment. At the moment, Herceptin can only be given with a taxane chemotherapy regime. But a grade 3 usually requires chemo anyway, so being HER2 positive just means an extra drug to fight the cancer. When they say agressive and invasive, they mean that a grade 3 is the fastest growing, but that doesn't mean there is a rush to get treatment started. Invasive simply means that the cancer has spread outside the duct, not that it has spread anywhere else.
I had ductal invasive grade 3, but I also had it in one of my lymph nodes. Mine was HER2 negative but oestrogen and progestogen positive. This means that now I have had surgery and chemo, I am taking a drug that will prevent my body from producing oestrogen. To put things in perspective, I had my surgery in December 2012 after being diagnosed in November 2012. I had chemo between February and May 2013. I have just have my first annual check and there is no evidence of cancer anywhere. So treatment does work successfully. So please don't give up hope.