DBA and General Contractor license
If I understand your question correctly you are looking to use the same corporation for two different businesses. Not being a licensed Florida law specialist I can only say that, unless there are any specific restrictions I am not aware of, you could in principle have a DBA registered for your corporation for the second business. I would, however, urge you to seek the advise of a licensed FL attorney prior to making such decisions.
Because it is one corporation its license should cover both businesses (you might need to notify the licensing authorities about your new DBA), however keep in mind that those two businesses are not separate entities - they both are run under one corporation. To separate the liability you would need to have a corporation for each business.
As far as insurance coverage goes I see no problem having two separate policies, but, again, not being an insurance specialist with knowledge of FL laws in that space I would recommend you to consult with your insurance brokers directly.