You asked what receipts you have to keep for your wife's travel expenses. There is only one circumstance in which you would need to keep any receipts. I'll get to it in the next-to-last paragraph below.
No matter what the company calls it, the "travel stipend" is really just additional pay. It should be included in your wife's paychecks, and included in the total wages on her W-2 at the end of the year. Since it's included in her pay, and not really connected with travel expenses, it does not require any special treatment on your tax return. As far as the stipend is concerned, there is no need to keep any receipts.
For your federal tax return, under the new tax law that was passed in 2017, for years 2018 through 2025, a W-2 employee cannot claim a tax deduction for any job-related expenses. Therefore, as far as the federal tax return is concerned, it will not be necessary for your wife to keep any receipts, since there is no deduction.
I'm not familiar with either Alabama or Georgia state taxes. Based on a quick look at the Georgia tax forms and instructions, it appears that Georgia also does not allow a deduction for job-related expenses. Florida has no personal state income tax. So there is no need to keep any receipts for either Georgia or Florida.
Based on a quick look at the Alabama tax forms and instructions, it appears that Alabama does allow a deduction for job-related expenses if you use itemized deductions on your Alabama state tax return. If you use the standard deduction on your Alabama tax return, there is no specific deduction for job-related expenses, so there is no need to keep any receipts. But if you use itemized deductions on your Alabama tax return, your wife's travel expenses would be deductible (subject to the 2% of AGI limit). In that case she should keep the receipts for all of her travel expenses for at least three years. (The Department of Revenue does not expect her to have receipts for things like cash tips, for which receipts are not normally given, but she should keep a written record.) Note that, if the employer correctly includes the travel stipend in her pay, it is not a true expense reimbursement, so all of her travel expenses are unreimbursed.
You didn't say anything about the Florida location. If she's going to be driving back and forth from home, that is commuting, not travel. Commuting expenses are not deductible, even on the Alabama tax return.
