Hello guys! So I have two computers at home a desktop and a laptop. The desktop has two user accounts: home(admin) and finance. The laptop also has two accounts as well: lap(admin) and children. My question is is it possible to remote desktop from home(admin) to children while being logged in as lap(admin) but not quitting the lap(admin) session on my laptop computer? Would the session quit even though I'm logged in as another user in that computer? Thanks in advance!!

You've got a couple of different questions here. First of all, you'll need Pro or Ultimate on the laptop in order to RDP into it; Home Premium doesn't support hosting an RDP session. When you RDP into a computer as a user other than that which is currently logged in the session doesn't quit, but the local user no longer has control of the machine. They'll regain control when you log out. This is the same as switching users on a desktop. The first user remains logged in, but idle, while the second user controls the machine. When the second user logs out the first user can log back in and resume their session from where they left off.

In general no. Using MS's RDP will kick out the current user. You can install VNC server/viewer. There are different freeware versions. You will be able to 'remote' into the other PC without kicking the user out. Install the server on the kid's PC and the viewer on yours.

Thank you guys so much! Your responses really helped!