I'm afraid there is no argument called extreme circumstance that can be put forward in drink driving cases. Your mother may be getting confused with an exceptional hardship plea, which can be put forward in totting up cases (where someone has admassed 12 points on their licence within 3 years) however this cannot be argued in drink driving cases.
Unless you can prove special reasons, which are commonly either, your drinks were spiked, you only drove a short distance, or there was an emergency, then a guilty plea carries a mandatory disqualification. Whilst your personal circumstances are definitely relevant in mitigation, they will not help you to avoid a disqualification entirely.
The sentencing guidelines for this offence advise a 12-16 month disqualification and a Band C, means tested fine. The Magistrates are also likely to offer you the drink drive rehabilitation course, which will reduce the length of your disqualification by up to 25% upon completion.