Looking to go to LAS for 7 days in November, if I go BA WT+ changing at LAX they want 6297 GBP

However if I go BA WT+ to LAX and then book my own flights to LAS they only want 1,237 GBP and I can get flights with America West for another 90 GBP.

I'm looking at leaving 3 hours between the BA flight into LAX and the onward connection and the same upon return.

Will this be long enough considering the security at US Airports these days and will we be able to collect our luggage and connect to the flights without having to go through security again or not ?

many thanks

Nigel