UK in Lexington definitely has Allen County newspapers, as I have researched them there. However, I just checked their catalog (which is online) and find that (with a couple of scattered exceptions) the earliest Allen County newspapers they have are from 1908, then 1911.
Frankly, I wouldn't hold my breath hoping that an obit in 1906 would be detailed enough to name a person's mother, but one can always hope.
Since it does not appear that there are Allen County papers extant for the time you need, consider whether there might be something published in a surrounding county -- especially a county that was close to where they lived and/or where they had connections: Barren? Warren? even nearby Tennessee.
I checked Simpson Co index for obits and neither Martha nor Harvey are listed.
Don't know what other work you have done on this, but you might want to check deeds, mortgages, court records for Barren County. There may be records (especially deeds) listing Philip's first wife there.
By the way, I note that there is a marriage for a Philip Carter in Barren County in 1844. So either your Philip had 3 wives, or there is another Philip Carter. So beware.
Sharon Meeker