I have a trip coming up and booked the following:

Outbound - Same Day
SLC-LAX (roundtrip ticket 1)
LAX-LHR (roundtrip ticket 2)

Return - Same Day
LHR-LAX (roundtrip ticket 2)
LAX-SLC (roundtrip ticket 1)

Is this allowed/a 'legal' booking?

In addition - if this is ok to do, would AA allow me to join the tickets? Or, will they allow me to check bags straight through from SLC to LHR on the outbound? Or, would I need t collect my bag in LAX and re-check it to LHR?

Any insight would be very much appreciated!