That location C:\WINDOWS\TEMP_avast_\unp195878148.tmp is where the avast scanner (avastSvc.exe) unpacks or moves files for scanning. That is as much as avast has to do with ownership as such.
Once avast had successfully scanned it removes those temporary files - the problem being avast won’t be able to either scan or remove them as it is essentially locked by the other AV scanner.
As Craig implies, this can be a classic case of a clash of resident scanners.
Yes you should certainly remove Trend - having an out of date security application is almost worse than not having one - no updates to correct bugs or virus definitions, etc. Not to mention what you have found conflict between two dogs fighting over the same bone.