BooBoo
Barcelona will eventually be moving to T3 but will be from T1 at the time your APs fly not T5 (although the LAX flight be to/from T5) so this will involve a terminal change for them if they stick with BA - the bags would, of course, be through-tagged to the final destination.
VS fly from T3 of course, but I don't think the Barcelona flight will have moved in time to be helpful to you.
BAH