In Berkeley for two months - enroll kids in school?

Welcome to Berkeley! I'd enroll them in public school even though you are only here for a short time. In Berkeley and other cities, you just need a local address (rental agreement) and they are then guaranteed an immediate spot in school. It might be a little disorientating for them at first, but it will give them something to do, put them in contact with other kids, and hey it's free!  There are so many families in Berkeley from other places in the world, temporarily and otherwise, that they will not be stand-outs.

You might be able to find some classes offered to homeschoolers instead, but I really don't think this would be better than being in public school, and it will be more expensive too.  This is a great opportunity for your kids to learn about adapting to a new place, and they might like it so much they will want to come back to our wonderful city for college!

I am a visiting scholar with 2 kids and I would strongly recommend you to enroll them to school and even to an after-school program (mine 6 years old attends a City after-school program in live oak park and loves it, and you also have after-school programs in each school). There are a lot of kids just spending some months in Berkeley (a lot of them are visiting scholar families) and the schools are used to deal with that.

Do your children speak English? My 6 years old didn't when we arrived here in August and now he does! There is a special program to help English learners to pick up the language. I don't know when your 11 years old is born (it is important because of the cut-off) but I would suggest enrolling them both (the 9 and the 11 years old) in primary school if they are English learners, it will be easier for the 11 years old to be an English-learner in primary school comparing to middle school.  

Good luck!

Welcome to the Berkeley area! I'm not sure if this would interest you but my kids attend a small independent co-op K-8 school in the hills on the El Cerrito/Richmond border called Crestmont.  It's a really cozy community where you could easily meet new families and have instant playdates with other kids.  Teachers are amazing, classes are small (around 15 kids), lots of intentional focus on social-emotional development and fun, project-based learning.  There are spaces currently available in some classes so you could email admissions [at] crestmontschool.org if you would like to consider applying.  We love Crestmont so please feel free to reply if you want to chat with me any more about it - I am happy to share more details about our experiences.

If you decide to go the homeschool route, there are also lots of great local resources.  There's a FB group Bay Area Homeschool Network that you could check out.  My kids have done camps at Sienna Ranch in Lafayette and the Ranch does classes during the year for homeschool kids as well - it's a really fun place.  There's also the In Addition+ micro school in Albany - I don't know much about it but it's popular among homeschool families too.

Best wishes with your plans!