If you're using TurboTax Online, clear your Cache and Cookies after the first import. If the second import uses the same Sign In credentials, however, it may import over the first one.
If the brokerage account allow you to choose what to import, you could chose the largest one (1099-B, maybe?) and make a one-line entry for the totals for each account for 1099-INT/DIV items.
In TurboTax Online, you can attach a PDF copy of your 1099-B to your return. For TurboTax Desktop, here's How to Enter a Summary in Lieu of Individual Transactions. This is perfectly acceptable to the IRS, since they have copies of all your 1099's.
Since you're having issues importing from two different brokers, here's How to Turn Off Anti-Virus Programs, which may be causing connectivity issues. If you can give more into about the error/message you get, we'll try to help.