Unfortunately Space Engine doesn't exactly seem built for this type of gameplay. However, I would suggest that you try out Kerbal Space Program, a very successful Indie game that is played by NASA engineers and has received many awards for it's physics engine and ability to build your own interplanetary rockets. It is also very moddable, so you can tinker the gameplay to however you want.
You can visit all the planets in the Kerbin system, up to and including the different moons. You can even get out of your rocket and walk around on the planets with a physical surface.
The spacecraft in the game are at a pre-alpha point of development. Their behavioural complexity and functionality is sure to improve with almost every successive release.
I'm sure at some point, there will be collision physics, docking ports, hard-pointed thrusters with visible (if the author desires) jets of propellant, rocket engines with atmospheric interaction modelled, separating and animating parts for spacecraft... it's only a matter of time, and Vladimir's continued interest in developing SE (which thankfully, shows no sign of abating).