This PowerShell oneliner will do the trick. You can remove the back-ticks and put the code all on one line if you want.
Get-ChildItem C:\data\*.* | `
Where-Object {$_.lastwritetime -gt '4/1/14' -AND $_.lastwritetime -lt '4/17/14'} | `
Remove-Item
I found a shorter version of the script here. I prefer to use the full Powershell cmdlet names though.