Misty Wisty,
Use Tools > Connect to put the verts anywhere on an edge.
Yes, sliding the verts affects the UV mapping.
Instead of redoing "create texture" use "ReMap UV". If that doesn't fix things... when you start UV_Mapping use RMB instead of LMB.
I have not used AutoUV that much so hopefully I am giving good info...
Edit: I see Fonte Boa responded before I got mine posted. Do what Fonte Boa said...
oort
Use Tools > Connect to put the verts anywhere on an edge.
Yes, sliding the verts affects the UV mapping.
Instead of redoing "create texture" use "ReMap UV". If that doesn't fix things... when you start UV_Mapping use RMB instead of LMB.
I have not used AutoUV that much so hopefully I am giving good info...

Edit: I see Fonte Boa responded before I got mine posted. Do what Fonte Boa said...

oort