Can you provide an example workbook?
If you have your sheets in a tiled dashboard, I find I have far less control over sizes and behavior.
I prefer to use floating for all my dashboards. Even if you just start out with a floating container that you resize to the entire boundaries of the dashboard. Once you are using floating containers, tableau lets you fix heights and widths and positions. If you have two sheets in a container, and if they are fixed widths, if you shrink the width of one sheet, the other moves to fill the space, but it keeps its original width.