Also, should I be concerned that there might be some type of limitation on coverage from either policy because of any sort of "coordination of benefits" between them?
-- Sorting It All Out
These are important issues to be concerned about -- before you get disabled.
My rule of thumb regarding taxability of disability benefits is to pay the premiums with after-tax dollars whenever possible. Then, when you are disabled, you will collect benefits on a tax-free basis.
Individual, or "private," disability insurance policies are almost always purchased with after-tax dollars, and therefore the benefits come to you tax-free. Group policies, where you pay the premiums on a payroll deduction basis, can be paid for with either after-tax or before-tax dollars. If the premiums are deducted from your gross pay, your benefits will be taxable. If they are deducted from your net pay, benefits will be tax-free to you. So, make sure the premiums are being taken out of your net pay.
Employer-paid administrative expenses to make the group insurance available to you won't affect the taxability of your benefits.
Your coordination-of-benefits question asks whether or not disability benefits received under one policy will reduce or offset benefits received under the other policy. Although it's quite common for medical insurance policies to have offsetting benefits, it rarely is the case with disability insurance. Group disability policies do often offset against Social Security benefits, workers' compensation benefits, other group insurance benefits, and so on, but they almost never offset against benefits from individually purchased, private-pay disability policies.
One final suggestion: Your private policy, which is "decades old," may have outdated coverage, such as not covering partial disabilities to retirement age. And although the sort of group insurance you have is usually a pretty good buy, it also might be lacking some important features. Seek out an insurance agent or financial planner with long-term disability insurance expertise to help you determine the adequacy of your current combination of policies and determine whether or not a supplemental or replacement policy might be needed.