First it is possible that you fail joining your personal PC to the Corp vpn. But, if you not, then is probably that you fail to connect each other.
The VPN have(must have) access list to permit traffic and chances are this traffic need to be permitted. And yet another problem exist with is called Hairpinning which means the traffic coming and leaving on the same firewall interface. This usually is not permitted also.
So, if you are allowed to connect both PCS, the easier way would be without VPN.
If your personal and corporate machines are in same LAN network, I assume you are taking RDP of the corp machine with private LAN IP. If the corp machine is already connected to VPN, it wouldn't allow RDP connection with VPN connected by default. If the behaviour needs to be changed, "Windows VPN Establishment" preference in VPN profile has to change to "Allow Remote Users".