MacBook Pro (13-inch, Mid 2010) Does not Enter Recovery Mode
Why don't you try bootable disk drive utility method;
Here is how this process works. First, it's necessary for you to prepare a USB flash drive. With that you can create and install a bootable OS X installer drive and then to fix Mac not working in recovery mode issue.
For that;
1.Reboot Mac and keep taping “Option” until you hear the sound.
2.Attach your bootable installer drive to Mac and choose it from the pop up list.
3.Then your Mac will restart and you are able to fix Mac.