The ex-Manchester United player denies using controlling and coercive behaviour and assaulting Kate Greville.
Mr Giggs, 48, also denies causing her actual bodily harm, and common assault of her sister Emma.
On his custody, he said: "I was scared, never been in that position before".
Manchester Crown Court heard a row broke out over messages to other women Ms Greville, 38, found on the former Wales international and manager's iPad in November 2020.
She left the hotel where they were planning to stay the night, and he decided to go home, the court heard.
When he got there he said he found the dog's crate in the open boot of his Mercedes car and he removed it.
"I quickly worked out they were trying to take Mac," he said, adding he was not aggressive.
He told the court he wanted to call the police but could not find his phone, thinking Ms Greville had it, which she denied.
Later, he said both slipped on bags on the floor as they tussled over her phone.
Ms Greville was on her back, and he was on top with his head at her waist, he said. He alleged she was kicking him in the head.
"I was protecting my head," he said, and after six or seven kicks he "got up" and moved away.
He told the court he was not initially aware of Emma Greville being at his home in Worsley, Greater Manchester.
After finding his phone, he put it in his pocket and did the same with hers. They then grappled in the kitchen as she tried to get her phone back.
He described how they moved around the kitchen island with Ms Greville grabbing for his wrist of the hand in the back pocket with the phones.
"It got more and more aggressive, it was a tug or war and we clashed heads," he said.
He said she accused him "of hitting her… of headbutting her."
Mr Daw asked him: "Did you put your hands on Kate's shoulders and forcefully and deliberately headbutt her in the face?" He denied it.
The court heard Ms Greville moved into his house during the first lockdown in March 2020.
His daughter and her boyfriend were there most of that time, and his son also stayed regularly.
Mr Daw asked about Ms Greville describing lockdown as "hell"..
But Mr Giggs called it "a really happy time from my perspective". They would "bicker" but had "no big arguments".
Asked whether he was "particularly keen on dishwasher loading techniques", Mr Giggs said it would often be on three to four cycles a day due to the number of people in the house.
"I would be opening the dishwasher and the tablespoons would be the wrong way round," he said.
"It would wind me up because I would have to do it again so I called a team meeting and just said, 'Everyone, can you please put the tablespoons the right way round'."
He was asked about an incident at a London hotel when Ms Greville claimed he threw a laptop bag at her head, kicked her out of bed and ejected her naked into the corridor.
He denied doing anything physical to her, said the argument fizzled out and "we more or less made up that evening".
The court heard they broke up for several weeks around Christmas 2019, but got back together and went on holiday to Dubai in February 2020, where they met her friend Katie Harvey for lunch at a hotel.
He said a row broke out in the taxi as they travelled back to their hotel after they had "been drinking rosé all afternoon".
He said with "a slip of the tongue", he called her by his ex-wife's name Stacey, but said it was not deliberate.
A row escalated and Mr Giggs said he asked her to leave their hotel, before changing his mind as it was just a "stupid argument".
However, she left and remained in Dubai with friends.
Under cross-examination, Mr Giggs accepted he was a hothead "on occasion" but denied being deceitful, self-centred and selfish.
He also said he sent constant messages to Ms Greville after she tried to break off their relationship, and would turn up uninvited to her home, office and gym.
The trial continues.