So to open this account, for which the bank has no risk, isn't providing overdraft, not extending any credit, etc., we must have a hard credit check done, and so we cannot do it that day.

Banks have some strict regulations to follow, so I would first think that they need to verify identities and such before opening accounts.

For "credit" on checking accounts, ChexSystems is used, not the credit agencies so much.

I backed her down on this, said I didn't care whether they called it a credit check or not, but they were going to use our Social Security Numbers to check something

Sounds like the regulation compliance I mentioned earlier.

This is some of why I hate banks. This is, in my experience, typical bank customer service.

While it is perfectly possible they didn't do their best to assist you, maybe your desires were not seen as something that valuable to them, and maybe you were the problem in not complying with their policies, many of which may be related to regulatory compliance.

They don't care in the least how many times I have to visit the bank to do something (like open an account); they don't care if my daughter won't be traveling here again for months

This is why I do online banking. You do not have to worry about any of these issues. Taking a day off to go to a bank to open a simple account seems wasteful.

If you are interested, I use Discover as my primary bank (although, not my primary credit card). It is easy to transfer money to and from accounts. Maybe your offspring would be interested in this? Or maybe you could set up an Internet account, so you could have the joint account and both have access at all times without concern for geography or time of day.

This is, in my experience, typical bank customer service.

Banks usually have tiers for different types of accounts. The lowest level consumer stuff is usually the lowest tier.