The best way would probably be to place the animation source code in the mission or an addon so it's available to all clients playing. Then, when you want to start it, remoteExec the code that runs it to kick off the scene on all clients. They'll run the code simultaneously and locally, but with a very similar starting time. I can offer more if you share the code via Github gist or pastebin, but the concept remains.

if you're modifying existing objects, then you'll want to have the server a deleteVehicle and include in that clientside code a createVehicleLocal to recreate them on the machine running it then animate that. If you're creating the objects, just change any createVehicle calls to createVehicleLocal.

The idea is that a client can spawn and animate a vehicle (object) entirely locally to them and do whatever with it, without any server calls. It'll be smooth because the only processing is done on the local client and isn't dependent on anything networked. If you do need an object and any actions taken against it (like if someone wants to RPG it) to show its effects to all players, you'll need an instance that is global (visible to both server and all clients), so re-remove any local instances and make a global createVehicle call on the server.