It is possible to be a member of more than one organization in Teams - for example your child might be part of a school organization, and you may be part of a work organization. Or you may be part of more than one school or work organization.
It is possible to switch organizations within the desktop or webclient (by selecting the organization name next to your profile picture, normally in the top right area of the Teams window). However this will not allow you to see messages from the other Team organizations you are connected to.
A simple workaround is this:
1) Open the desktop client and connect to whichever organization you prefer
2) launch the webclient version of teams (either from teams.microsoft.com or your office365 apps page)
3) If prompted, select webclient option
4) You will not have both the desktop client and the webclient open. You can switch the webclient to connect to any other organization you want.
It is possible to have multiple webclients open at the same time, all connected to different Teams organizations.