There are several questions that you asked.
For federal income tax, it is generally better for spouses to use joint rather than separate status. For those cases where is it better to file separately the only real way to know is to prepare all three returns (one joint and two separate and compare the joint result to the total of the two separate results).
Federal income tax will use all of your income and deductions regardless of what state it is in. Child support is not income that is included for income tax.
Since Florida does not have a state income tax and you are still a resident (with your stationing in Vermont temporary) as a nonresident of Vermont you do not include your military pay for full-time active duty with the armed services and do not include your income earned in Florida on that state return. See http://www.state.vt.us/tax/individualmilitary.shtml
Since your spouse is not a resident and has no Vermont income, you can file a separate return in Vermont. If your only Vermont income is active duty military pay you will not have any Vermont income subject to Vermont income tax.
Not quite sure what you mean when you wrote " I did taxes earlier this year, and the online turbotax software said that I didn't have to claim the income that I'm getting from the renters? That didn't seem right, but it checked out at the end when reviewed by the software?"
Generally you will have to enter the income and expenses for the year and only if there is a net profit will that net income add to your other income for federal income tax. So, it may be you had more expenses than income for the rental which is why it did not add to your other income.
The rules for losses on rental are involved but when gross income is more than $150,000 the losses are usually not allowed and some can be when income is less.
There is an exception from including rental income if you only rented the property for fourteen days or less during the year. Nothing is reported for that short rental period.
From what you have described it seems that a separate Vermont return for you and a joint federal return is probably best in your circumstances.
Please ask if you need more discussion or information.