Since your available source is 3:2 (2304 x 1536 pixels), you will have to address photo cropping as well as resizing since you are not going 3:2 to 3:2 or 4:3 to 4:3 or 16:9 to 16:9. You are aiming at 3:2 to 16:9.
If you take a bunch of 2304 x 1536 3:2 photos into Photoshop Elements Full Editor File Menu/Process Multiple Files, then the end result will be distortion (stretching of the objects horizontally). Try it putting an image with a circle through the resizing process oftered there. I always make a distinction between scaling and resizing for these purposes. Process Multiple Files is a convenient batch route for resizing but does not offer batch cropping. And, although I see batch resizing, I do not call that the batch scaling that you seek.
You could look at the free program named IrfanView for batch cropping and batch resizing. But I do not see where any of these batch cropping approaches can be a one size fits all operation.
It would seem that you would get the best desired effects with one by one, tedious as it seems, if you cannot get the look you want otherwise. These one by one to which I refer might include:
a. If your computer resources permit, importing each photo into your 16:9 Premiere Elements project and "scaling" it to fit the 16:9 space established by the project preset in the Edit area monitor (Default Scale to Frame Size unchecked in preferences or in the file option by right clicking the Timeline file.)
If you opt to scale each image in the Edit area monitor space, you can use the file's Properties Palette/Motion Panel expanded Scale property either Width and Height scaled together or separately. To do the Scale Width separately from the Height, remove the check mark next to Uniform Scale there.
Cropping individually followed by batch resizing is one alternative to getting "batch" in the workflow somewhere. Why bother with the batch resizing as a second step when you can do crop individually with resize in the same step in Photoshop Elements Full Editor with its Crop Tool?
Please review and consider. If any questions or need clarification, please do not hesitate to ask.