how large, massive, far away (from earth), and fast would an object (planet-like) have to be to block out the Sun for 3 hours and not disturb Venus, Earth, or the Moon?
Is it possible? Not really. Not with your criteria. Could some mad scientists make it happen, like if we make the Moon bigger? Er, maybe.
Nasa's eclipse page (scroll down for maps over 20 year periods).
2001-2020 map below.
The map has a notation for hybrid eclipses (see here), not all that relevant to the question.
Total solar eclipses (blue lines on the map), are quite small because the umbra or fully shaded region that the Moon casts on Earth is small, maybe 150 km in diameter on average, 267 km max. All planets and objects that orbit the sun cast an Umbra that extends behind them. The Moon (diameter 3,474 km), is always casting an umbra somewhere in space, being about 1/400th the diameter of the sun, it's umbra is about 1/399th the distance between the sun and the moon, or roughly 375,000 km on average. Eclipses happen on Earth when the Earth is lined up below the Moon's Umbra. Mostly they don't line up which is why eclipses are rare, but the Umbra is always somewhere in space, not all that far from the Earth, following the moon's path.
Your scenario mentioned planet-like. Now, if it's a planet from our solar-system, that would imply disturbing the orbits of Earth/Venus/Moon, which you specified you didn't want. There's also real danger if you were to have a planet like object in a near Earth orbit that passes from time to time, close enough to cast it's Umbra over Earth. For safety reasons "just passing through" is the way to go.
A rogue planet on a hyperbolic trajectory past the sun that, by very rare coincidence, passes between the Earth and the Sun, but close enough to cast it's Umbra over Earth would be very rare to say the least, but a theoretically possible scenario to cast a total eclipse over Earth, but it would need to pass very close and at just the right angle to block the 1/2 of 1 degree of arc that the Sun takes up in the sky.
Mars is roughly twice the diameter of the Moon, so would need to pass within about 750,000 km to the earth, and line up just right, to cast a tiny umbra that moved across the Earth.
Venus, about 3.5 times the diameter, about 1.3 million km
Jupiter, about 41 times the diameter of the moon, would need to pass within about 15 million KM to cast an umbra on the Earth of similar size to the typical Moon's eclipse Umbra.
And those are the minimum distances. You'd need the theoretical planet to be pretty well inside those limits to have an Umbra of significant size and for a 3 hour eclipse, bigger is better.
What would a rogue planet passing that close look like?
Consider that it's passing close enough that it looks larger than the Moon, at least for a 3-plus hours. How close it would need to be depends on the size, as noted above.
The minimum velocity for an object on a hyperbolic trajectory just passing through the solar system but near Earth distance would be Earth's escape velocity, or the orbital velocity of the Earth (108,000 kph) times the square root of 2, and if it approached on the same plane and in the same direction as the Earth, the relative velocity between this Rogue planet and Earth, the minimum relative velocity would be about 45,000 kph, give or take. That's absolute bare minimum as a theoretical rogue planet passing inside the Earth's orbit would usually be traveling a fair bit faster than that.
So, for a planet like that to remain between the Earth and the Sun for 3 hours, it would need to be about 3 times 45,000 km in diameter, or, nearly the size of Jupiter.
A small rogue planet couldn't cast an Umbra over Earth anywhere close to 3 hours because it would pass over the Earth much too quickly. A Jupiter-sized Rogue planet could, theoretically, if it was closer than closer than 15 million km, cast it's umbra over Earth for 3 hours or so, but that would be close enough to change the Earth's orbit and, at the very least, give the Earth significant climate change by pushing the Earth a few million km either closer or further from the sun. Not an ideal scenario.
So there's no scenario that does what you ask. You'd need a planet the size of Jupiter, with the mass of Neptune or perhaps less to leave the Earth/Moon undisturbed. A Neptune mass planet with a large ring system . . . just maybe. But given how rare your scenario is to begin with, I'm going to say basically no. You could do it, but it would change the Earth's orbit, or you could do it with a smaller planet but for much less than 3 hours. In any case, it would be a preposterously rare scenario no matter what.
What if we move the Moon?
With rogue planets, I just looked at the relative velocity between the planets, which is close enough for a near-sighted umpire. When you look at the Moon's umbra, the Moon's motion is much slower, so you also have to take into account the Earth's rotation too.
The Moon (Synodic period), takes 59 minutes to cross the sun, that's tip to full cover, and another 59 minutes back to tip. (based on a 29.5 day synodic orbit, 29.5 days to cover 360 degrees, the sun, roughly 1/2 of 1 degree in the sky). So, 158 minutes of partial eclipse, and a record, of 7 minutes total eclipse in one spot on Earth (7 minutes, the record for a total eclipse is possible when the Moon is slightly larger than the sun, close to it's perigee).
So if our mad scientists pull the moon closer to the Earth, the period of time for a total eclipse increases but the rate that the Moon moves across the sun also increases, so you're effectively increasing the 7 minutes of total but decreasing the 158 minutes of partial. If you pull the Moon all the way into a geostationary orbit, some 10.5 times closer, the Moon would span an enormous 5.25% of the sky, but it wouldn't move in the sky while the sun would and the sun, which crosses about 1 degree of sky in 4 minutes would pass behind the enormous geo-stationary moon in just 21 minutes. You can't create a 3 hour eclipse by pulling the Moon closer.
This is where the Earth' rotation speed comes in. The Moon moves over the Earth in it's orbit at about 3,683 kph, and relative to the sun, but because the Earth is in orbit to, the effective velocity relative to the sun (Synodic not sidereal) is about 8% less.
The Moon's umbra effectively moves with the Moon's relative velocity - at least, close enough.
The Earth rotates in the same direction that the Moon moves, peak velocity at the equator of a bit over 1,600 kph. In effect, the rotation of the Earth tries to keep up with the movement of the Umbra during an eclipse, but the Umbra moves West to East about twice as fast as the Earth turns West to East.
So the solution for your 3 hour eclipse? Make the Moon bigger and push it further away so it orbits the Earth more slowly and it's Umbra moves closer to the Earth's rotation speed, making a 3 hour eclipse, at mid day, close to the equator . . . possible.
If we replace the Moon with Venus (3.5 times the diameter of the Moon) and we push it some 3 times further away (which would be pushing the limits of the stability of the Earth's hill sphere), then you'd be a lot closer, as our new "Venus Moon" would move across the sky and across the sun still to fast, but it would move more slowly and closer to Earth's rotational velocity leading to eclipses that stayed in the sky much longer. If you did that, you might get your 3 hours of total eclipse. You wouldn't want to push Venus too far, cause you'd want it a big bigger than the Sun in the sky, but 3 times the Moons distance, it would be about 15% larger and close to the limit of orbital stability.
Other silly ideas.
Now if you were to Move the Planet Uranus into Earth's L1 Trojan point, which . . . well, the Trojan point would be further away due to the larger planet's mass dominating so . . . that wouldn't work and because L1 points aren't stable, it would also be highly dangerous. Moving on.
If you were to move Uranus to where the Earth is and make the Earth a satellite of Uranus . . . we might get longer than 3 hour eclipses every time we were on the far side of Uranus making an orbit. Seems a lot of work though just for an eclipse. . . . but that would work too.
OK, I'll stop now.