Tell us a little more about what you're trying to do more specifically.
I can't figure out what your problem might be. What you're exactly describing is just not possible. Exactly what timeline are you referring to? Every object has its own "timeline."
You can keyframe just about every aspect of anything in Motion (there are few exceptions!) All keyframes belong to the "object" (group, layer, filter, behavior, etc..) that you set. Their "timeline" is the life of the object. They can only be moved with specific keyframe editing [*the Keyframe Editor]. The exception being Behaviors which set keyframes automatically so you don't have to (which can only be changed by parameter settings or by converting to keyframes which removes the behavior from the layer.)
Layer objects can contain masks, behaviors and filters, Each of these items can contain their own keyframed parameters. While all of these attached items belong to and will ALL move WITH the layer when it is moved, if you select them in the layers list OR the Timeline window and move them, they move independently of their parent layer. That will throw your keyframing out of sync, but the keyframes for that item will not change relative to its beginning..
IF you are talking about keyframing a layer object and MOVING it to another group, then yeah, it will look like it has been reoriented because it is being moved from one space to another space. Each group is its own "universe" (even subgroups within subgroups) and coordinates are local to it. Getting into this jam is easy to do and can be a very frustrating aspect in Motion.
Not knowing exactly which rut you're stuck in I can't really be much more help. Mostly it comes down to be careful what you drag. Otherwise (in the case of transplanting one group into another group) there are methods of editing in a group's local 3D while still within a parent 3D space... [I say 3D even if a group is actually 2D because Motion accommodates apparent 3D orientation/perspective within flat planes with layer order.] In all cases, keyframes do not move in time - they stay set relative to the object they are attached to. I've been using Motion for eight years and I've never seen a keyframe move on its own no matter how its object gets moved in time. And moving a single object, or even changing any of its keyframes will never change another object's keyframes... unless you've linked them with a link behavior (or some other behavior that's dependent on the object being moved)... and that's a whole other kettle of fish; but it really doesn't sound like you're "there" yet.