Stream is a plugin from XWP which works, but compared to newer security audit plugins such as WP Security Audit Log, it is quite limited. Stream can also bloat the site database, depending on how long logs are being stored by.
To reset the database of entries that Stream has created, you can do so from wp-admin;
Stream > Settings > Reset Stream Database
When you deactivate and delete the Stream plugin, the two custom database tables that the plugin creates will not be removed, unless you click on the uninstall next to the plugin in the plugin list.
An easy way to delete the two Stream database tables, is to use WP Optimize plugin to delete those.
WP Optimize > Database > Tables
Search for stream, which will then find the following two database tables.
After you have removed those two db tables in WP Optimize, when you click on the refresh button, no tables will be found.
Now you can install and activate the free WP Security Audit Log plugin on your child sites. MainWP has a free extension for WP Security Audit Log called Activity Log for MainWP. There is already a complete post, which covers the Activity Log extension in great detail.
Migrating from using Stream as your site activity log to using WP Security Audit Log will give you more information in your site log as well as less bloat in your sites database.