You have not posted enough information for us to help you.
What version of Premiere Elements and on what computer operating system is it running?
What are the properties of your source media? Is the project preset set to match the properties of those
What are the details of your export of that Timeline content?
Please describe "video shake"
a. As in camera shake
b. As in interlaced ghosting
c. As in pulsating of the frames (edges or throughout frame)
Do you see this problem in previewing before export? What is your player?
Is this a "it worked before but not now" or "it never worked before" issue?
Let us start here. Please review and consider and supply details.
Any questions or need clarification, please do not hesitate to ask.