What version of Premiere Elements are you using and on what computer operating system is it running?
The answers will be in the details.
While we await the details, I will guess that you have Premiere Elements 11 on Windows.
If that is what you have, where are you - in the Expert or Quick workspace.
If you are in the Expert workspace, look for the Timeline Indicator (red stem, blue head). Highlight the clip that you want to split. Then hold your mouse cursor over the stem of the Timeline Indicator. About half way down that stem you should see a tab. The tab shows the scissors shape. Click on that to split the clip at the place of the Timeline Indicator.
Another approach would be to move the Timeline Indicator to the spot to be cut, and then use the keyboard shortcut of Ctrl+K.
Same principles are involved in doing this in the Quick workspace.
Please review. If any questions on this or clarification needed, please do not hesitate to ask.
I do not understand your problem with the Tools. So, we may have to go further into that with more details.