If the machine has AVG already installed you can just check the box next to the machine and click "Install." This will reinstall AVG with having to uninstall, reboot, and reinstall.
If you remove AVG first before reinstalling, you will have to reboot before attempting the install. I'm going to assume that your installation options have the checkbox "Reboot the computer after installation if needed" checked. If you do, this will force reboot the machine if you have not rebooted it already after the uninstall. You can find this option in the Install/Remove section; click "Installation Options" in the top blue bar and uncheck that box.
The above mentioned reinstall will circumvent this issue. Some nodes may require a reboot after reinstalling, but I have not yet run into that problem.
Please let me know if you have any other questions!