I have been experiencing this same behavior since upgrading to version 10.
I opened a support ticket and they pointed me to a link to download Version 10.0.1 (27695).
I installed the new version and it seemed to fix my problem initially, but the problem began happening again.
I seem to have found a workaround for the moment.
I find that if I shut down my virtual machine in Parallels Desktop and then start it up, I can connect to remote computers using Remote Desktop from within the virtual machine and my modifier keys (shift, ctrl, alt) work as expected.
If I "suspend" my virtual machine and then resume it, when I connect to a remote computer using Remote Desktop, the modifier keys only work after typing more than one key while holding them down.
For example, if I open Notepad, hold down the shift key and type three "t" characters, instead of it coming out as TTT, it comes out as tTT.
Again, this only seems to happen if I "suspend" my virtual machine instead of shutting it down.
At least I have a workaround for the moment, but I prefer to use Suspend instead of Shut Down, so I have sent a follow-up message to Parallels support to let them know what I've found.
Hopefully it will help them recreate the issue and can patch it.