The problem is in the local group policy. They are applied to all. there is no way to direct the group policy to a specific account on the local policy. If you have an AD domain, then you can apply to groups that you and the second account a members of. This is due to the policy being a file on the machine that when turned on, is applied to all. It wouldn't make sence to only apply it to one user on the machine, when it's design is for network based deployment.
You can look at the Group policy configuration, %systemroot%\system32\grouppolicy\machine or User \\ registry.pol
that file contains the local policy configs. Once you have configured it, if you look at the file, then extract out what you want to use, you can create that into registy settings that will not be true policy, but work the same way. They are just easier to get around.
Hope that helps.