When you open a (running) VI in a sub-Panel, it shows the Front Panel of the VI as it is when it is running. So there are a few solutions to your problem of "showing only the yellow part":
I'm pretty sure (I actually tested this for a change 🙂) the VI gets a panel resize event (and successive pane resize events) when it's inserted into a SubPanel. This will automatically move splitters with the SubPanel's rectangle as new panel bounds. Fit to pane controls will also resize, and I don't think there's much you can do about it (except turn off fit to pane).
I'm not 100% certain I know what @wiebe means (I'm quite sure, though, he's probably correct). I remembered, however, that there was a step I forgot to include: When I want to put a Front Panel in a sub-Panel, I measure the width and height of the Decoration, and the width and height of the sub-Panel, and "manually" resize them so they "fit" (i.e. are the same size). Actually, I don't really "measure" -- I take the VI with the sub-Panel and the VI with the "Front Panel + Decoration" that will be put into the sub-Panel and slide the second VI's Front Panel "on top of" the one with the sub-Panel to make sure the sizes are the same. I often size the sub-Panel and Decoration so they are an integer number of "grid blocks", which make the comparison easier. A little bit of work, but the results are very nice ...
I think that would work in general, but I don't think it will work with splitters.
I can test what happens if you change the panel bounds after inserting the VI in a subpanel... If that works, it is a solution to OP's problem.