Hey, I`m not sure if you got this issue fixed, but I found a solution as I was looking to open the developer tools on the right as well.
In the bottom left of your screenshot you will see a button that opens the developer tools in another window. If you click and hold that icon, you will see an option to dock to the right. Drag your cursor over the dock to the right icon that appeared so that it is highlighted. and there you go it should be docked to the right now.
Hope that helps