You're probably okay because you have a 12 month visa. Make sure your son files the tm-30 each time you return to stay with him. You can most likely get a residency certificate from that tm-30 but probably good too have him write a letter that you are staying with him long term. Immigration like documentation...
Take all that with you too the bank. Dress reasonably and act professionally and if you don't get an account at the first bank, try another. Use the main branches in the town you're living in.
A certificate of residence is issued by immigration. Bring 1 passport photo, copies of your passport bio and visa pages and a copy of your lease agreement.
Seasoned funds don't need to be foreign. But you will need bank statements showing when they arrived and your passbook showing the funds are still in your account on the day you go to immigration for your extension.
If you were applying for your non-o in country then the funds would have to show as being from a foreign source.