Still few details... so I'll weigh in with a semi-educated guess...

Concentrate on UA. My rough approximations are:

Trip to Europe = 11000 miles
East coast = 5100 x 3 = 15300 miles

That mileage alone makes you Premier. You'll then have access to Economy Plus and occasional free domestic upgrades. Plus you'll have the best flight schedule options out of SFO and access to Star Alliance for awards.

The six flights a year to Southern California would be no more than 6000 miles. Doesn't really move the dial in this equation. So it would be fine to keep using Southwest for the schedule options (including OAK)... or fly on UA...

As far as credit card choices, consider:
UA Select Visa for the UA tickets (3 miles/$) and their 2 miles/$ spending categories
2% cashback card for everything else

You could also use the Southwest Visa for your hotel stays and rental cars. They pay 2 points/$ for their partner hotels and car agencies. Then you could use those points to pay for your SoCal trips.

It only makes sense to use a branded hotel credit card if you're going to stay with the same hotel chain all the time. Otherwise the Southwest card is a good option.