Did Qui-Gon and Obi-Wan know that Padmé, masquerading as a handmaiden, was actually Queen Amidala

I've always felt like she kept it from them as well. Not because she especially distrusted them, but because it was just best to play her cards close. That said I always felt like Qui-Gon knew, he was just smart enough to expect it, and Obi-Wan was clueless about it.

Oh she definitely had all of them fooled. It wasn't until that bold move with the Gungans that everyone found out. Even first-time viewers were tricked.

See, having handmaidens who could operate as both bodyguards and possible stand-ins hidden in plain sight was a security idea thought up by Captain Panaka soon after the young Queen took office. It was an old practice that had not been used in over a century on Naboo, but the practicality of it made sense. That, and it is not commonly used among royalty or high-ranking officials on a lot of planets. In fact, it seemed an odd idea for security, considering how peaceful Naboo was. But Panaka was smart in realizing that there was always a risk that his ruler could still get hurt in some way or another, regardless of how peaceful his homeworld was.

I mean, when you look at the Queen and her handmaidens, all you see is a woman with a very elaborate outfit on, with several young ladies similar in age to her, in low-key robes, silently following her around. The first thing a lot of people are gonna think is "Those are her servants, her retainers, maybe even her ladies-in-waiting." And that would be an easy assumption to make, since it's not common to see a royal or high-ranking politician without at least one personal helper of some kind. Most have their bodyguards in armor, standing discreetly off to the side, and most do not have body doubles hidden among the serving staff.

The last thing anyone's gonna think is that each one of those girls was trained in combat, espionage, and how to masquerade as the Queen. Her big costumes and white makeup help a lot, as does training all of them to talk and behave similar to her if need be. The only way the ruse could be ruined is if the chosen decoy isn't that good in diplomacy, or doesn't understand the intricacies of political discussions, as what happened with Boss Nass. Or worse, they do something the Queen would not do, and a sharp-eyed person noticed.

Pretty sure you can't hide from The Force.

Yeah, they were fooled as well. I mean they couldn't even detect the presence of Darth Sidious whenever they were in Palpatine's council chambers, even after Dooku spilled the beans in Episode II and declared a Sith Lord in charge of the Republic to Obi-Wan.

I feel that it was pretty strongly implied that Qui Gon was aware of the decoy charade but simply went along with it. When Padme protested that the queen wouldn't approve of them risking so much on the hopes of some random boy they just met winning pod race, Qui Gon just cheekily tells her with a slight smirk that the Queen doesn't have to know about it, basically daring her to drop the ruse. Qui Gon & Obi Wan also don't look at all surprised when Padme reveals herself to the Gungans.