Reporting somewhat depends on how the deed was held. If both mom/dad were on the deed, when dad passed, automatically passes to mom. When mom passes and you inherit it, the FMV at time of mom's death is what you would use reporting your cost basis for the sale.
However, if you were added to the deed at some point before mom's passing, then mom 'gifted' half her cost basis to you. If that happened in 1983 when dad passed, yes, you would need 'adjusted basis' on that date to determine the cost basis of your half. The adjusted basis would be half of her cost basis of $7500, plus the value of improvements (reasonably FMV). It might be a problem determining this number for 1983. Old tax records may need to be reviewed.
If you sold the property, then your cost basis is half the property FMV at time of mom's death, and half at FMV at gifting date, so your attorney is on the right track, if this is the case.
You would add the cost basis of each half together to determine your Cost Basis and any gain/loss at time of sale.
Gifts are reported to the IRS (but generally not taxed) by the giftor so they can track them. If you 'gift' over 1.2M, then the giftor is assessed tax on their gifts. A Form 709 would be filed separately from a tax return, but since the giftor is deceased, it does need to be filed. It may have even been filed the year of the 'gift'.
@sheryljo
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