YouTube has quietly made a new web-based video editor available to signed-in users, one that can trim and paste together uploaded clips into new works. If you need a backing soundtrack, YouTube’s got free audio tracks for that, too.
It’s a pretty straightforward linear video editing tool. Select a clip you’ve uploaded, trim it to length, then stick it in the video timeline. For audio, you can drag and drop in some of the free tracks YouTube has available from the AudioSwap library, and edit those clips, too. It seems adequate for splicing together Ye Olde Family Vacation, and any other fairly straightforward video topics you may have broken into multiple parts.