Can I indicate that some of the proceeds from my mother's IRA were distributed to other family members? If so, where?

[kjh07tax-]

Distribution is under my SSN, but funds were split between 3 additional family members.

[MaryK4]

If you were the beneficiary, you are responsible for reporting and paying the taxes.  You could have determined the tax due before distributing to your siblings, or request they pay you now.  

[dmertz]

The amounts that you gave to others are gifts from you to them.  If the amount you gave to any one person in 2022 exceeded $16,000 you must file a gift tax return, 2022 Form 709.

As MaryK4 said, under these circumstances one would typically gift amounts net of your marginal tax liability rather than amounts in proportion to the full gross amount.