How would I make a part move while its being moving randomly

So I have a pet and I am scripting it to animate but the question is I have a part that is connected to the dragon and for animating purposes I use tweenservice. Now to change its position while its moving (for animating purposes) so that I can complete the animation. If anyone has a answer please tell me!

Can you make the question more clear?

Do you need to do half of the tween and then move the pet and continue it?

so I want the pets wings to flap while the pet is being moved by the player.

Something like this:

I suggest use an animation to flap the wings and you can just ween or lerp the pet to the player with a certain offset

All I need to know is how would I make a part move with the model even tho that part is tweening its rotation/position just like that video;.