Piotr, however, has news for his critics. He realises that life is physically tough for his 21-year-old daughter and has advised her to retire by the time she reaches her mid-twenties. "This is such hard work," he said. "Professional sport is not good for your body. It's not healthy. This is my daughter. This is a heavy thing for a young person to do every day. If you have a job, of course it's better to work from nine till three in the afternoon rather than until eight in the evening."
He added: "Your tennis career is very short. I've talked to Caroline about this. For me, if you have won Grand Slam titles or achieved your dreams, stop when you are 25 or 26."
Wozniacki has already achieved plenty. Although she has not won a Grand Slam, she has won 18 tournaments and was world No 1 for a total of 67 weeks.
However, at a time when her boyfriend, Rory McIlroy, tops the golf world rankings, Wozniacki has slipped from world No 1 at the start of the year to No 8, her lowest position for nearly three years. She has gone nine months without winning a tournament.
At the end of last year, when Caroline was still world No 1, Piotr finally stepped aside and she started working with a new coach, Ricardo Sanchez. The Spaniard lasted less than two months. By the beginning of February Piotr and Caroline were back together again, though she is also doing some work with the adidas team of coaches.
Piotr, who insists that he would still be happy to loosen the reins, said his daughter never wanted to bring in a new coach. "Caroline talked to me beforehand and said, 'Please don't change things. For me the best situation is if we stay like this.'
"But I talked to her several times and tried to convince her that this was a good idea. Caroline told Sanchez, 'Ricardo, this isn't easy because I've been with my father for the last 15 years every day, for several hours a day.'
"It's normal that Caroline should be very close to me. And it's the same with me. I understand every small detail with Caroline. I know when she's happy, when she's unhappy. I know whether I can change that or whether I can't. I know whether I can push her or not."
Like many father-coaches, of whom there are plenty in women's tennis, Piotr is self-taught. He played professional football in Poland and Denmark, which became the family's home after he changed clubs.
Caroline started playing tennis at seven, but Piotr did not coach her until she was 14. If there are deficiencies in her technique, he says he knows where the blame lies. "For seven years, until the age of 14, Caroline played this way," he said, demonstrating a clumsy forehand. "She served this way. She didn't play slice. She played these two-handed volleys on both sides. She played five metres from the baseline. This is what Denmark did for Caroline. At that time we thought these were the best coaches in Denmark."
He added: "Caroline isn't someone like Steffi Graf or Martina Navratilova. She comes from Denmark, which has no tennis culture. It's not a country like Sweden, for example, which has produced many players."
He watched and learned for seven years, talking to players and coaches. "I saw different things," he said. "After this we made some changes – small things every day. But once you have played in one way and with one technique for seven years from a young age, it's not easy to change. There is no chance you can change everything in one day."
As for her passive game style, Piotr said Caroline was more of a big hitter in practice. "Ask Andy Murray and Novak Djokovic," he said. "They've practised with her sometimes and said, 'What is this? Is this a woman?' Caroline is ready [to play this way], but this is only practice."
Piotr thinks she can learn from Murray and Djokovic. "Andy Murray's tennis is close to Caroline's, but Andy is playing counterattacking tennis better and better," Piotr said. "We're looking to play the same way. He is a good example. Djokovic also played similarly to Caroline, but he's now a bit more aggressive, playing further inside the court. But it takes time. Djokovic is 24 today, but people were talking about him as a champion when he was 17."
What specific changes could Caroline make? "You might see her coming into the net more. Caroline could play slice to change the rhythm of a rally, not just as a defensive shot. She can be more accurate with her first serve. She can hit more of a kick second serve."
Piotr defended his daughter's demanding schedule – only Marion Bartoli exceeded her total of 80 matches played last year – but admitted to one big mistake, when she played in Brussels the week before last year's French Open. "When Caroline lost to [Daniela] Hantuchova at Roland Garros, I could see in her eyes that she was tired and had no more energy," he said.
"In one or two more years there's no chance that we will play so many tournaments. I'm not stupid. I understand about recovery and about travelling between different countries. It's not easy. It's only easy for people sitting at home and watching it all on their television while drinking a beer."
Caroline's lack of success has coincided with her relationship with McIlroy, but Piotr said he was a good influence. "I'm happy that Caroline is happy," he said. "They are two people who are very professional. I can see when Rory stays with us sometimes how he practises every day and works on things, as Caroline does."
Fathers and daughters in women's tennis
Maria Sharapova
Father Yuri took Maria to train in Florida when she was nine, meaning she was separated from her mother for two years. Often criticised for coaching from the stands, Yuri caused a stir in Melbourne with a throat-slitting gesture after Maria's victory over Justine Henin. Maria is now coached by Thomas Hogstedt.
Agnieszka Radwanska
Was coached by father Robert from the age of four but stopped travelling with him last year and has since climbed to No 3 in world rankings, winning titles in Dubai and Miami. "We had some arguments off the court," she said. "Professional tennis is always a lot of stress and emotions and everything."
Marion Bartoli
Will not be at the London Olympics after a fall-out with French federation, who would not allow her father and coach, Walter, to work with her at Fed Cup matches. At Wimbledon last year Walter was fined for coaching from the sidelines and during one of her matches he was asked to leave the court – by Marion herself.
Jelena Dokic
Was reconciled last year with father Damir following an eight-year rift. He coached her from an early age, and had many run-ins with tennis authorities. He also spent almost a year in jail for threatening to blow up the Australian embassy in Belgrade and possessing illegal weapons.
Aravane Rezai
Rezai, a former world No 15, has not been the same force since the 2011 Australian Open, when her father, Arsalan, who has clashed with tennis authorities and other parents, was banned from tennis. Aravane later filed a complaint against her father, for "harassment, intentional violence and death threats".
Paul Newman
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