If you already have Visual Studio 2010 installed on your development machine, you do not need to download a separate installer. You can simply copy the required files directly from your Program Files directory to the remote machine:

My.VisualStudio.com 64-bit Standalone (Mirror): CNET Download (x64) 32-bit Standalone (Mirror): CNET Download (x86)

Open the x86 or x64 folder depending on the remote machine's OS.

To ensure a successful connection between your local and remote machines, follow these configuration steps: Configure Visual Studio 2010 Remote Debugger

While Microsoft has officially moved older downloads to the Visual Studio Subscriptions portal (requires a free Dev Essentials or paid subscription), you can still find the standalone installers through reliable archive mirrors:

Microsoft Visual Studio 2010 Remote Debugger Alternative: Using Local Files (No Download Required)