The Italian authorities concluded Claire Martin killed herself after suffering from post-natal depression.
Her parents, from Sutton-in-Ashfield in Nottinghamshire, believe she was murdered because "things don't add up".
Ashfield MP Gloria De Piero said there are "anomalies to explore".
Ms Martin, 30, lived with son and her in-laws in Grottaminarda, near Naples, while her partner worked in Germany.
In March 2012, Ms Martin suffered multiple stab wounds to her neck, struggled upstairs and died.
A murder investigation was launched, but 15 months later the Italian authority closed the case after it ruled she had committed suicide.
Following a recent Guardian newspaper article on her death, her father Ray Martin said: "Things don't add up.
"It's impossible to stab yourself multiple times in the neck and climb up stairs after wiping the blood clean off the knife."
Her mother Pat Martin said: "It's a continuing nightmare, nobody gives a damn."
Ms De Piero said forensic reports have been translated into English, but there are witness statements and other evidence only available in Italian.
The MP has asked for a meeting in October with the Italian government to "get the answers the Martin's need".
Mr Martin said: "We hope to meet with the magistrate, but I honestly don't know why they won't speak with us."
The Foreign Office said it would not comment on individual cases, but has provided consular assistance to the family.
It added: "We will continue to assist in any way we can, although we cannot interfere in the legal system of another country."

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Scotland scored twice in three minutes in the final quarter to win 2-1 in Glasgow.
James Carson gave Wales the lead from a penalty corner, but Ben Cosgrove and Alan Forsyth won it for the hosts.
Earlier the Wales women's team lost 3-0 to Italy to finish fourth at their EuroHockey Championships in Cardiff.
Chiara Tiddi, Celina Traverso and Federica Carta scored the Italian goals.
"We came out fighting for the bronze today but just couldn't hit the line," midfielder Sian French told BBC Wales Sport.
"We'll keep on pushing as a team for the next two years and we'll come back even stronger next time."
Because two teams get promoted from the B Division, Wales's men will compete in Europe's top tier at the next EuroHockey Championships in 2019.
On Friday, Wales women's hopes of rising into Europe's top tier were shattered in a 2-1 defeat by Russia.
Wales' men secured promotion to their top tier by beating France 4-3 in their semi-final in Glasgow.
Wales women had beaten Austria and Poland, but lost to Belarus on the way to the semi-finals.
Neither Wales side has been in the EuroHockey A Division since it was reduced to eight teams more than a decade ago.
The nation's women were playing in the third tier just four years ago.

The blaze started at the ICL UK Boulby mine at 00:30 BST on 13 April, 1,100m (3,600 ft) under the sea bed and five miles (8km) from land.
Seven workers were taken to hospital and treated for smoke inhalation.
The Health and Safety Executive (HSE) said a notice had been served in relation to the underground fire.
More than 100 staff were underground at the time, 11 of whom were temporarily unaccounted for.
Polystyrene blocks are believed to have caught fire in the mine.
A spokesman for ICL UK, said: "We have been working closely with HM Mines Inspectorate in the investigation into the recent incident.
"Safety is always our first priority and we are fully committed to working with the inspectorate in order to identify ways in which procedures can be improved.
"We will, of course comply with all the measures set out in the improvement notice."
The company has until 27 June to comply with the notice.
The HSE said the investigation was ongoing.
One of Europe's deepest mines, the site employs about 1,100 people.
Last year, the company announced it was shedding hundreds of jobs as part of a "new business strategy" to produce fertiliser polysulphate.
An MP has written to Prime Minister David Cameron in her bid to establish how a suicide verdict was ruled after a British woman died in Italy in 2012 from stab wounds to the neck.
[NEXT_CONCEPT]
Wales men's hockey team suffered an agonising late defeat by Scotland in their EuroHockey Championships II final.
[NEXT_CONCEPT]
A potash mine in East Cleveland has been issued with an improvement notice after a fire broke out hundreds of metres below the sea bed.