I've been having a very similar issue on my hardly used Windows 10 running the January update. It kept failing the February cumulative update, and then after multiple failed attempts and temporary fixes, it went straight to April Cumulative update (which you are trying now), failing miserably again.
I've tried multiple solutions suggested online, on Microsoft support pages/forums, and other tech related sites, and in the end it's the Windows Update repair tool run 3-4 times in a row with reboots in between that has done the job.
To give you an idea of what did not work for me:
1) sfc /scannow (no errors found)
2) windows disk system clean up
3) DISM command repair (once again no errors)
4) multiple Windows update reboots/redownloads
5) manual Windows cumulative update download
6) built in troubleshooting tool in Windows
7) "SC config trustedinstaller start=auto" command
8) Service Stack update
This is the support page that helped me resolved the problem, after a few attempts:
https://support.microsoft.com/en-gb/help/10164
It took a few runs and reboots to get it sorted.