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)