Here is a bit more information. The video files came from a Sony Handycam HDRCX760E AVCHD and a Medion Action Cam.
My computer 16GB Ram, CPU Intel Core i7 2.2GHz, Nvidia Geforce GT540M 2GB.
Premiere Elements 13 on what computer operating system?
For now, assuming Windows 7, 8, or 8.1 64 bit.
What are the properties of the videos that you put on the Timeline, and what project preset did you set manually or did the project set automatically to match the properties of these source media? If you do not know, please tell us what you see for Edit Menu/Project Settings/General and the readings for Editing Mode, Timebase, Frame Size, and Pixel Aspect Ratio (even if the fields look grayed out).
To try to zero in on the properties of the source media, please name the brand/model/settings for the cameras that recorded these videos - this is easier than downloading and installing properties readout programs to find the information. If bitrate readings available for the source, please post that information also.
When you played back the rendered Timeline before export, did you see problems in that play back in the Edit area monitor?
For export, what was the specific export settings Publish+Share/Computer/AVCHD - what preset, and did you use the default settings for that preset or customize the preset under the Advanced Button/Video Tab of the selected preset?
When you did the burn to DVD - was that DVD-Video format on DVD disc or AVCHD format on DVD disc?
Let us start here and then we can decide what next.
I did not see the name of your cameras until have I had posted (post numbered 2). Please give the camera settings.
Are you working in a PAL rather than NTSC setup?