I think the problem can be solved, but maybe there isn't enufe information about what you are wanting to acheave.

and also Strarup has a good handle on how to find out exactly what your dealing with to resolve the problem.

ok from what I understand you want to delite the edge that gose down the side of your object there right ? but when you do it changes to that bit of twisted looking like there are to objects there.. ?

ok a cuple of points to consider.. just becouse you combine to poly objects in to one object. that dosn't meen that there are not in fact to seprat poly shells ! to combine a shell in to one true object/shell you have to merge the edges or vertices.. useing the merge tool, or a booline operation.

about the poly going a bit crazy on you.. your object(s) could be behaving badly becouse I noticed you have just one face there on the right side of the ofending edge you want to do something with. that has one face showing but there are.. 21 edges for just that face. That could very well be why your poly acts wierd. it is one poly face that is true, but becouse of the way that the computer and grafix card acualy have to make that it it finds its self not sure how to comply with your wishes.. as the true geo that is displaed is made up of triangles. only 3 sides.. so when there is a face with that many edges it gets to ware it can not acualy make it corectly.

sorry if long winded but I hopel its more understandable.