Nicola Hawkins' dad John, 66, chose to end his life on September 27 after an 18 month battle with the incurable disease, which his late father, also John, died of.
Assisting a suicide in England and Wales is illegal with a maximum sentence of 14 years.
But Labour's Kim Leadbeater is introducing a private member's bill to legalise it, which is to have its first reading in parliament today (Wed).
MPs are likely to have a first vote on the bill at the end of November after calls from campaigners such as tv star Dame Esther Rantzen.
John's dad John had a "nasty fall" after his diagnosis and John was scared that he would also become ill and wouldn't be able to fly over to Switzerland.
So he decided to fly over there before he planned to so Nicola, 24, believes she would have had more time with him if assisted dying had been legal in the UK.
Nicola said: "The laws in the UK meant that I had less time with my dad. I could have still had months with him.
"But the fear of him being trapped in the UK after a nasty fall like my grandad made him go sooner than he'd like to have gone.
"I was robbed the extra few months with him.
"I don't believe anyone truly understands assisted suicide unless they have a family member go through Dignitas or a loved one pleading for their suffering to end.
"Watching a loved one die suffering when they are fully aware of what is happening and are being forced to stay alive should not be the norm for this country.
"I really hope it's legalised. I don't think any argument is strong enough against it."
Nicola says she and her mum Lynn Hawkins, 56, now fear being arrested by police because assisting someone into suicide at Dignitas is illegal in the UK.
Nicola said: "Now me and my mum are waiting for the police to come and knock because what we did is illegal.
"My dad tried to talk us out of coming with him multiple times due to the thought of us being arrested for going with him. He made a brave decision that day.
"He must have been so scared, knowing he was doing to die but the thought of him doing that alone is heartbreaking."
John's dad, also called John, was also diagnosed with MND and died from the disease in 2012, aged 79.
So because he knew what would happen to him, he decided he "didn't want to live through that" and made the choice to have an assisted death.
Nicola said: "Because his dad had it, he knew the outcome. He was a really active person before the diagnosis.
"I watched him go from running around Ennerdale, a lake in Cumbria, to being sat down on the sofa with a neck brace on.
"He said if he hadn't seen it with his dad, he might not have made that decision but because he knew what would happen, he didn't want to live through that."
Nicola says she is still coming to terms with the loss of her dad, a former chemist, and the fact that he will never walk her down the aisle or meet her children.
She also said it was "horrific" watching him die and that his last words were "I love you."
Nicola, of Oldham, Gtr Manchester, said: "It's always just been us three - me, my mum and dad.
"We didn't want him to go but the alternative was much worse.
"The only thing we could do is support him.
"It was horrific. It's the fact we were so far away.
"We sat and held his hands and his last words were, 'I love you'.
"Just watching him die - I don't think anyone is prepared for that.
"After he died, we had to leave. You're over 800 miles away.
"We didn't have the support with us and had to get back on a flight.
"When you've just lost someone, it's really hard to do."
John's brother Mike Hawkins, a Labour councillor, says his brother's decision was "very brave."
He added that he hopes assisted dying will be available in the UK, as long as the "right checks are in place."
Mike said: "When you listen to John's story, basically since he got his diagnosis, he's had to plan his demise.
"If it was available in this country, he could still be alive today and would still have a good quality of life.
"He could have put that to the back of his mind and enjoy what he had left.
"I didn't want him to do it but you can't know what it's like until you're in that situation.
"It was totally his decision. He was very brave.
"My view is now that it should be available in this country after seeing what he went through.
"I think for a civilised society, we definitely need to start that debate.
"I can understand people's concerns but as long as the right checks are in place and it's safe, I would support it."
Dame Esther, 84, who has stage four lung cancer, thanked supporters who have kept the issue at the top of the political agenda this year.
The star, who has signed up to Dignitas, said it would help people "not to shorten our lives, but to shorten our deaths".
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