Just to give details that might be different than your situation:

1.  I am the bookkeeper but I sign into Quickbooks as the owner.  We have only one sign-in we use between us.

2.  "Updating" QB accounts doesn't always work right away, especially if have changed or edited the connection, eg. didn't work yesterday when I changed connection but did today.

3.   I recommend disconnecting and re-connecting fresh each time you delete, add or edit the bank accounts you are downloading, eg. one of our credit cards changed numbers.  I had to delete the entire connection in QB with bank and re-connect (bringing up our four bank accounts including the new credit card account).  This is most important lesson I learned, lol.

4.  The only way you can avoid having to press the "Push" button for you bookkeeper is to add her to your bank account at a level about equal to yourself.  I was not comfortable to do that so we live with the "Push" situation.  Basically, I text him to "Push" when needed which is not always convenient for him.

5.  I asked the bank to add my phone number as an alternate to him but they don't have that function yet except as co-account holder.

I know this doesn't make life perfect but hope your functionality improves.  Let me know if you have any more questions.