EXCLUSIVE: Doting dad Michael Lockwood - without his trademark hat - takes his twin daughters dress shopping at Target as he fights estranged wife Lisa Marie Presley's sensational claims he had a stash of child porn on his computer

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It’s a picture of parental devotion - a doting father taking his precious little girls out for an early dinner and then on to Target to buy a new dress.

But this day out on a cloudy day in Southern California was different.

The eight-year-old twins are Elvis Presley’s granddaughters and their father is having to defend himself against sensational claims that he had a stash of child porn on his computer.

And while their parents throw bitter allegations at each other in court, the girls, Finley and Harper Lockwood, are living with their grandmother Priscilla Presley.

Michael Lockwood and his two twin daughters Harper (left) and Finley (right) stepped out in Santa Monica on Sunday for a daddy-daughters outing. Lockwood bought Finley a new striped dress, which she wore out of the store

In papers revealed exclusively by DailyMail.com last month, The King’s daughter claimed that she found ‘hundreds of inappropriate pictures and disturbing video’ on Lockwood’s computer

The trio ate an early meal at the Mexican restaurant Lula, before heading out for a quick shopping trip at Target

But no observer could have guessed at the discord when musician Michael Lockwood took the girls out on March 12. First he took them for a Mexican meal at Lula, a restaurant a block from the beach in Santa Monica before going shopping for a dress for Finley.

The girls’ mother - Elvis’s only child, Lisa Marie Presley - had picked the girls up from Priscilla’s home in Beverly Hills the previous day, as she got her time with the twins.

Presley, 49, and Lockwood, 55, her fourth husband, are locked in a bitter divorce battle following the collapse of their 10-year marriage.

In papers revealed exclusively by DailyMail.com last month, The King’s daughter claimed that she found ‘hundreds of inappropriate pictures and disturbing video’ on Lockwood’s computer.

But rather than give Presley custody of their daughters while it investigated her claims, Child Protection Services decided to take the girls from both parents and agreed that they could live with their 71-year-old grandmother.

‘The girls have not been in foster care and never will be,’ Priscilla said in a statement. ‘The girls have been with me and will be until all this is sorted out.’

Priscilla, who sources say is siding with her son-in-law rather than her daughter in the divorce battle, said both parents see the girls regularly.

In the court papers, Presley said: ‘I was shocked and horrified and sick to my stomach,’ when she saw the images on Lockwood’s computer.

But her husband shot back, blasting her for making the ‘unproven allegations’ against him in publicly available papers.

Lockwood, on the other hand, blasted Lisa Marie for making the ‘unproven allegations’ against him in publicly available papers

‘As I experienced during our more than 10-year marriage and as I believe this court will learn [she] has great difficulty being honest and she rarely, if ever, accepts personal responsibility for her own wrongdoing,’ he said, also asking for Lisa Marie to pay his legal fees for the matter

‘It is particularly distasteful that [Presley] has placed more value on trying to damage my reputation than on the fact that her false statements may be brought to our daughters’ attention,’ he said.

Michael Lockwood was missing his trademark hat on his outing with kids.

‘As I experienced during our more than 10-year marriage and as I believe this court will learn [she] has great difficulty being honest and she rarely, if ever, accepts personal responsibility for her own wrongdoing,’ he added.

Lockwood was asking for $100,000 from Presley to pay his legal fees and $40,000 a month in spousal support, but in court papers her lawyer, Mark Gross, argued that she should not have to pay, partly because of the pictures she said she found.

He also cited a post-nuptial agreement the couple had signed which Lockwood argues should be torn up.

Presley claims nearly all her money is gone and she is living with her daughter, actress Riley Keough, in her home in the Los Angeles suburb of Woodland Hills.

Last week a judge ordered she should pay him $10,000 a month for legal fees and is still to decide on spousal support.

Presley and Lockwood, 55, a musician who has worked with Carly Simon, Fiona Apple and Aimee Mann, among others, were married in a lavish $340,000 ceremony in Kyoto, Japan in 2006. Her first husband, Danny Keough, was the best man.

The girls looked happy to be with their father, despite sensational allegations against him from their mother Lisa Marie Presley, and Harper skipped down the street while holding Lockwood's hand

Happier times: Presley and Lockwood, 55, (pictured in 2011) a musician who has worked with Carly Simon, Fiona Apple and Aimee Mann, among others, were married in a lavish $340,000 ceremony in Kyoto, Japan in 2006

After they split last June, their amicable relationship quickly went downhill. In his court papers, Lockwood also said Presley - who was also married to Michael Jackson and Nicolas Cage - is hiding a vast fortune by pretending to be broke. At one time she was said to be worth $300 million

They separated last June.

In his court papers, Lockwood said Presley - who was also married to Michael Jackson and Nicolas Cage - is hiding a vast fortune by pretending to be broke. At one time she was said to be worth $300 million.

He claimed she still receives $466,000 a month (or $5.6 million a year) from the trust Elvis set up for her before his death in 1977.

He said her tax returns showed that from 2013-2015 she also got more than $4.5 million a year in dividends and capital gains and she receives way more than the $100,000 a month that she claims.

He said in the same three-year period he earned an average of just $55,017, ‘less than one percent’ of her income.

Now he said he cannot find work because Presley insisted he concentrate on her career throughout their marriage. ‘The music industry changed during that time and I lost most or all of my professional connections,’ he said.

‘Further, I believe [Presley’s] allegations in her declaration will ruin my reputation and it will be difficult or impossible for me to get a job.

Lockwood even slammed his wife over her claim that he had bought the twins an expensive, fully-stocked saltwater fish tank. He said there were just two goldfish in the small tank.

Presley arrives at Narita International Airport in Japan in 2014 with daughters Finley and Harper in tow

He said cell phones she claimed he had bought them cost $18 each from Target. ‘They play with them,’ he said.

‘I continue to live a below poverty line existence and need financial assistance to pay my expenses, and my fees and costs,’ Lockwood added.

Presley had claimed she was broke and that forced her to move in with her daughter.

She said she hadn’t been on a plane in 18 months and couldn’t remember the last time she bought ‘clothes and shoes of any value.’

She said Lockwood and a business manager had defrauded her of millions of dollars and she now owes $7.3 million in back taxes and has another $655,000 of other debt, including $212,000 owed on credit cards.

Presley listed 11 bank accounts, mainly held in banks in Jacksonville, Florida. One has just $6.50 in it and another has $9.88. The amounts total nearly $105,000.

In her filing, Presley mentioned only Coes Hall, her home in Sussex, England, saying it was worth just $2 million, while she owes more than $5 million on it.

But Lockwood said she ‘failed to disclose material information and attempted to mislead the Court.’

He said she has been paying for five other homes: three in California, one in Franklin, Tennessee and one in Hawaii.