One table and only one table is directly associated with a given layout. The only ways to effectively do what you describe is to:
a) set up relationships such that you put a portal to each table on a panel.
b) simulate the slide control with a different layout for each table such that changing panels actually changes layouts. The slide animation probably wouldn't work for this, but tab controls are sometimes emulated in this way.
Since filemaker supports hundreds of layouts without issue, I think it's a bad idea and you're just creating a lot of unnecessary work for yourself.
Is animation really an expectation of your solution?
Sliders can be useful. For a main layouts with details or lists, a layout based on the table occurrence is a better way to go. Data display and scripting should be easier.
That stated, sliders can be very useful in the same way a tab object is. Showing selected data or portals when needed and hiding it when not.
I thought I could use the animation between slides, but you are all right, it is not wise to do something like that.
Too much pain, too much work, for something that is questionable.
Thank you for your help.