Time to revisit this:

How did Michael persuade Vincenzo to leave his "two-meal town' in Sicily and appear at the Senate hearing/ And why did a single glance from Vincenzo to Frankie convince Frankie to renounce his affidavit? Your views?

I think the 'persuasion' is obvious: somewhere in Sicily, Vincenzo's grandchildren are being 'looked after'. And the glance was just to shame him. My views.

I think the Sicilian aspect played a big role in Frankie's decision.

1) Frankie was actually born there,and was, at heart, an old-school Mafioso.

2) When he saw his brother, I think it made him realize how far he had fallen from the values of the Tradition he had been a part of.

3) I think it was more his brother's shame than anything else that was communicated in that brief glance.

4)Knowing that he ( Frankie) would forever be known in Palermo as a rat,and that Vincenzo would be ostracized by everyone in his world,not only during his lifetime ,but the lifetimes of his children and grandchildren as well,was unacceptable to 5 Angels.
Don't forget,Sicily was the land of Vendetta.There was bloodshed between families over things like the theft of a pig committed by long dead ancestors.

Also Frankie says that his brother could have had his own Family,so I assume that the concepts of Honor, Family, and Omerta were very well ingrained in him, and Frankie's betrayal would have destroyed everything he lived for and believed in.

I think Vincenzo probably came voluntarily, believing family honor was at stake. And I think Frankie was already ambivalent about testifying, and so didn't need much to push him in a different direction.

I agree with all.

I think Michael dispatched Tom to Sicily to inform Vincenzo about his brother’s infamia, and to persuade Vincenzo to come to Washington to “aid his brother in his time of need.” I infer that Vincenzo was a gabellotto, from Frankie’s description to Tom: “He’s ten time tougher than me…he could have been big here, he could have had his own family.” So, Michael (through Tom) didn’t have to threaten Vincenzo—he would have seen immediately that when word of his brother’s betrayal of omerta and his own Don reached Sicily, Vincenzo’s hold over his “two meal town” would weaken, and his enemies would stop at nothing to get rid of him, even, as LucaB said, kidnapping or killing his grandchildren. I bet Tom didn’t have to work hard to convince Vincenzo to come to Washington.

As Pete astutely pointed out: Frankie was already wavering about his testimony before Vincenzo appeared: The first thing we see him saying to the FBI guys is, “Ten to one -- ten to one shot you said -- ten to one shot he would take the Fifth -- and I lose.” Sure—all the mobsters that the FBI guys hauled before Congressional hearings took the Fifth, so they told Frankie that if Michael did, he wouldn’t be needed as a witness, and his survival and betrayal of Michael would be kept secret, at least for a while. Credit Roth’s evil genius for knowing that Michael’s obsession with “legitimacy” would prevent him from ever responding to accusations of his criminal past with “I decline to answer that question because my answer might tend to incriminate me” [emphasis added]—especially before a televised hearing. Hence the brilliant perjury trap Roth set through Questadt and the committee chairman that Michael fell right into.

And as Lou said, it all came down to Sicily, honor and family. Once baleful glance from his brother and Frankie recovered the Tradition he grew up with and lived by. As Tom said to Vincenzo after the chairman adjourned the hearing: La honore di la famiglia sta posto—“The honor of the family is intact.”

While all of that is probably true as Vincenzo saw it, Frankie new the other side of that coin: keep your mouth shut or Vincenzo gets it.

Sure thing Vincenzo would have been horrified, to learn of his brother Frankie's "betrayal of omerta and his own Don" [not public knowledge? at that time] unforgivable infamia in their honour is everything! world

and Vincenzo would have come to Washington on his own accord
Frankie was jolted and reminded of omertà by his brother Vincenzo's presence, his piercing icy stare was knifelike
Made Frankie realise, what he was about to do - betray his Don - is a no-no in the business they have chosen and need to honour the omertà

Sure thing Frankie was wavering
As regardsMafia's code of conduct and ethics! – No kidnapping or killing of women and children

I wonder when Mike made this plan. Was he always planning on trying to bring Frankie’s brother over or was it after his talk with Fredo

My guess is that as soon as the Senate chairman says there's a witness who can impeach Michael, they figure out that Pentangeli is the only possibility. They may have been kicking around what to do about him before they left Washington.

The chairman was very helpful! telling Michael about their secret star witness
Did anyone else notice that .......

Star witness -- Frankie Pentangeli who “has had no buffer between himself and Michael Corleone”

Michael's "perjury rap"
my take, too since Michael already knew that Frankie Pentangeli was alive and was being prepared in custody to testify against Michael – the committee's secret star witness when Michael went to talk to Fredo -- arrangements would have already been put in place,
1. to bring Frankie's brother, Vincenzo over or
2. Vincenzo was already on a plane, to the Senate hearing