Hi bryanktracy1!
The new withholding tables and method of calculating the withholding can be tricky for employers to learn. It is quite possible that the new employer had the withholding calculating incorrectly. The Form W-4 and method of calculating withholding changed in January of 2020. Employers are still learning the correct calculations. If all the information was virtually the same (salary and W-4 selections), then both employers should calculate roughly the same amount of tax. I'm glad that your wife was able to submit a new W-4 with the "additional" amount so that she can have some withholding coming out of her paycheck. You may be able to find a paycheck calculator tool online to check the withholding. Here's a link to one that you may want to try:
https://www.adp.com/resources/tools/calculators/salary-paycheck-calculator.aspx
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