You should be able to append and delete with topology tables. It could be you have to turn off the option to instantly validate your edits. However, some times I am required to be in an edit session to do geometry or field calculations. Whether this is due to relationships or topologies in those files would be hard for me to test. As a better workaround, you can essentially append within an edit session by using the Load Objects (aka Simple object loader), which is an older append tool for ArcMap or ArcCatalog.
... View more