If you don't want to drive it, you'd have to pay for LAX-SAN on AA or UA, as has been mentioned, the codeshare is for connections and cannot be booked as standalone.

If you were to book the whole ticket as a UA or AA ticket, you could book it all as one circle trip. Since you want to fly CO, and CO doesn't serve LAX-SAN, it would likely fare higher, as you'd be paying for an open-jaw on CO and a one-way on UA or AA. This is where CO's west coast weakness is can cost you.

Faring Example (UA or AA ticket):

CLE-ORD-LAX (1/2 RT CLE-LAX)
LAX-SAN (1/2 RT LAX-SAN)
SAN-ORD-CLE (1/2 RT SAN-CLE)


Faring Example (CO + UA/AA segment):

CLE-LAX (1/2 RT CLE-LAX)
LAX-SAN (1-WAY LAX-SAN)
SAN-IAH-CLE (1/2 RT SAN-CLE)

So, in the first example, since you're flying wholly on UA or AA, UA or AA will essentially cut you a break on that stopover, charging you half the RT on that segment (probably about $75 more than the open jaw) since you're flying the whole ticket on UA or AA. But if you book CO, and combine an AA or UA segment, you get hit with a one-way on that segment, or about $250 extra over the straight open jaw.

My suggestion: Drive it. It's a couple hours in a one-way rental car. Alternatively, choose a West Coast stopover point in a market where you can get a cheap one-way fare on your alternate carrier. If the fares in that market are one-way fares, you won't be penalized for flying a different carrier on that portion of your trip. For example, while AA charges $250 for LAX-SAN, they charge only $65 for SJC-LAX-SAN. So a SJC stopover will likely be cheaper. But if you really want to beef up the miles, AS is a CO partner and lets you fly SJC-SEA-SAN.