Vicky Liggins had taken her 19-month-old daughter to West Midlands Safari Park in Bewdley but as she drove through the Asian rhino enclosure she thought the animals were getting too close.
A few moments later, a rhino came up behind the car and smashed into it. Vicky put her foot down as her daughter Evelyn and her sister Beth Rees screamed in terror – but the rhino gave chase.
The family eventually got to safety after a ranger came to the rescue, but the rhino had caused £500 damage to the Mitsubishi Warrior 4x4.
The safari park has apologised to Vicky and have sent her £250 as a goodwill gesture.
But Vicky, 26, who lives in Halesowen, wants barriers erected to prevent rhinos wandering in front of vehicles.
She told the Birmingham Mail: "We were absolutely petrified. I dread to think what would've happened if we'd been in a smaller, lighter vehicle.
"As we drove past the three rhinos, I thought they were too close. These animals are two tons - they weigh more than a car; they're dangerous animals.
"I didn't notice the rhino behind my car until it hit the vehicle with its horn.
"We were all really frightened. It then shunted us from behind with such force that the back wheel lifted off the floor.
"We were absolutely petrified. I thought the rhino was going to pierce the back panel and smash through the rear windscreen.
"We couldn't drive away because of the rhinos in front.
"My daughter was in tears and the sad thing is that she loves animals.
"I want the public to understand the dangers of safari parks. Even with so called 'rangers' on site, it isn't safe."In an official statement to the Birmingham Mail, the safari park has said sorry, but has declined to go into detail about the incident.
A spokeswoman said: "The highlight of a visit to West Midland Safari Park is to drive amongst free-roaming animals and to get the chance to feed some of them. In addition, we also offer a guided minibus tour for a small extra charge.
"We welcome many, many thousands of visitors during the course of a year without mishap and, therefore, we are very sorry that wasn't so on this particular occasion".