@Fiscal Manager KLCCOA 

"This starting to sound simple to me, but I am having trouble getting the funds to show up in the P&L the way I want and go in and out of the bank accounts correctly for reconciling.

Can anyone help with this?"

Is the Edward Jones (EJ) investment account a business account?  If so, the income is recorded as the offset when you increased the EJ Investment balance at the time of the transfer to Bank Account 1. Debit EJ Investment, credit Income or, if you recorded unrealized gain, debit unrealized gain, credit income.  Then, it's just a transfer from Bank 1 to Bank 2. 

The expense is recorded when you enter the bill in QB.  Then pay it from Bank 2. 

You didn't mention if you're on cash or accrual basis but using a bill and paying it from Bank 2 will allow QB to accurately report the expense on either basis.