I live near Santa Barbara, about 3 hours from LAX (depending on traffic

)
I would like to fly BA from Phoenix with companion coupon. There is more availability from there. US Air has multiple non stops to Phoenix.
I do not think that US Air and BA work well. Is there a problem with a RT to Phoenix then Phoenix -> LHR and beyond? Bags? Late flights?
Sorry if this has been asked and answered, it is hard to search this.
BTW- I really like BA. I won 10 business class tickets and have had several free upgrades.