Sarah Fellows was told by the judge at Mold Crown Court on Thursday: "You could have killed people driving your vehicle."
The 36-year-old, of Burgoyne Street, received a 10-month suspended jail term and was banned for two years and until she passes an extended test. She must also undertake rehabilitation and 180 hours of unpaid work.
The single mother had admitted dangerous driving, failing to provide a specimen and criminal damage to a police car window.
Judge Niclas Parry said she had collided with two cars in an "extremely dangerous, prolonged piece of driving" – adding that she had been "hopelessly drunk".
But the judge said: "This is also a sad case for reasons I need not go into. You acted on that day in desperation. Mercifully, no-one was harmed.”
Prosecutor James Coutts said another driver in Llangollen Road, Trevor, in Wales, came up behind a Vauxhall Zafira going "significantly" slower than the 60mph speed limit and veering on the wrong side of the road, including on a blind bend.
Opened bottles of alcohol were in the Zafira.
The court heard that Fellows’ behaviour had been “erratic” on the way to police custody. She was unable to provide a breath test and refused to give a blood sample.
Andrew Green, defending, said Fellows had suffered a “trauma” in her early life and turned to drink.
“She’s truly remorseful for how she behaved,” he said.