You will have to pay Virginia tax on the income that you earn for the days that you work in Virginia. You will have to file a Virginia nonresident tax return.
There are a few states that tax remote workers, but Virginia is not one of them. So you would not have to pay Virginia tax for the days that you work remotely.
You didn't say what state you would be working in when you are working remotely. I assume it would be Florida, in which case you would not have to pay any state tax on the income you earn for the days that you work remotely. If any other states are involved, post details.
If your LLC is a single-member LLC that has not elected to be treated as an S corp or C corp, then as far as state income tax is concerned it doesn't matter whether you work as an employee or an independent contractor. But, of course, if you are a contractor you would have to pay federal self-employment tax on all of the income, no matter what state you worked in.
