Since there is too much of what would go weird should the system be subjected to the real world's physics, I assume that there is some magic at work that helps stuffs retain their properties, namely air in space, zero gravity between worlds (there is NO place without gravity in the universe, and the smallest object at the farthest place does apply its gravity "here" wherever that is), suns with less mass and apparently no friction vs interplanetary air (also no gravity close to them?), etc. Therefore, the plain answer to your question is a definite YES, as in, you CAN reach the other planet on an ordinary aircraft, but...
But, spacefaring devices would still not be like intra-planetary aircraft, namely because there is place with no gravity, thus no "down" and "up" which have to be accounted for when designing aircraft. Wings would serve no purpose out of gravity, engines would have their thrust vectors off mass center with no compensation from control elements, making a normal airplane start rotating under its own thrust with a sudden inability to normally control the flight. A helicopter with added means of orientation control could do, however. I assume that a "rocket" with twin rotors like on a modern attack helicopter like Ka-52 on its top would be the correct shape for an interplanetary spacecraft within your world set. You can control thrust with copter's normal means of control, you can drive through "space" on the same rotors, you can control turn in zero gravity using rocket's fins (retractable if they spoil travel while in a gravity field), additionally you can use smaller airplane engines to turn your rocket sideways, once in another planet's gravity field, you turn the "bottom" of the rocket towards the planet and start an almost normal helicopter landing.
The main problem with such travel would still be fuel. The space is BIG, your air-filled space might not be that big but still, there would also be currents in intra-planetary air that could easily shun a vehicle off course by too much to miss the destination, there could be rogue asteroids barely seen in space because the ambient light would not let your spacecraft see them before they would have no time to dodge the collision, there might be dragons (Chinese type) afloat in midair that prey on unsuspecting travellers or whatever life that could exist there as well, and all the mentioned and not mentioned dangers would ask for fuel expenditure to avoid. A helicopter's normal flight span is limited in hours, yours might take a day or two worth of fuel, yet still it might be too small to reach the destination. There is a possibility however, use a VERY large rotor that's powered by rocket passengers' muscle force, with zero gravity and low air resistance air-rowing is quite a method to provide a little bit of speed. In fact, such a rotor could well serve as fins when the craft is powered by engine. But, this type of travel would be even slower, and would expend the rocket's food storage together with fuel. Hmm.
Regarding planet gravity of 2-3 Gs at ground level, you can alter the planet's atmospheric density to allow flight in such conditions, and thus design your aircraft to both withstand this gravity construction wise, and fly in dense air using normal aerodynamics. Note however, since the density curve for an ideal gas in a gravity well is a frikking EXPONENT, and for a real gas it's close to that at relatively low pressures, you need to design your gravity wells somehow to allow nonzero values at their edges and not too high values at the bottom, otherwise floating would surpass heavier-than-air flight for both lifeforms and aircraft. After that, the answer to your question of "can ordinary aircraft reach another planet" would shift to a no, as a floater cannot properly move in zero gravity, or would break down while lifting from the dense atmosphere.
Regarding interplanetary travel for lifeforms - the answer is yes, provided they can feed on something mid-flight. Otherwise, they would run out of fuel (fats and other energy within a living body) and die in mid-air. There's a multitude of issues with such a travel however, first the movement in air at zero gravity is something different from flight (close to swimming underwater, in fact), which birds might not be able to learn, while insects and seeds/pollen might reach the other planets by intra-planetary currents; second, the navigation problem - unless your midair is EXTREMELY transparent, your planet dwellers would not be able to see the sun(s), probably the nights if any would also be very weird. Here on Earth, when you look at the sun, there is about ten kilometers of dense air obscuring sunrays, in your world it would be millions of kilometers of dense air, making the intra-planetary medium opaque. There might be more problems, requiring more time to analyze, but I believe this set of problems would first need to be solved before you continue.