how to group together images to move them across a page?

so i'm doing an animation, and i have two title texts i want to alternate between (to create a sort of film scratchy effect), but then i want to slide this text across the screen. I'm wondering if there is a way to group together the images (i know there's a group action but this doesn't work for this) so i don't have to adjust the positions of each image to be in place for the next image.

soooooo

what i want to do is alternate between two images, and have that alternation slide across the screen.

i know there is the possibility of exporting the switching between two, and then slide that one exported clip, but is there a way to group images together in premiere alone?

thanks!