You mentioned receiving a Form 1099-R. That means that there was a distribution from a retirement account that is taxable to the beneficiary that received the distribution. The code in box 7 of the Form 1099-R indicates the type of account from which the distribution was made. Code 4 with the IRA/SEP/SIMPLE box marked indicates a distribution from a inherited traditional IRA. Code T or Q would indicate a distribution from an inherited Roth IRA.
If mutual fund shares are distributed in-kind for an inherited IRA, the taxable amount (value) is still taxable to the beneficiary. The mutual fund shares then acquire a cost basis equal to their value on the date of distribution and their holding period begins on the date of distribution, equivalent to selling the shares inside the IRA, distributing the cash, then repurchasing the shares outside the IRA except that the shares are treated as non-covered shares. A subsequent sale of the shares outside the IRA would be reported on Form 1099-B.
"Were my mom still alive, I don't expect she would have to pay taxes on the full value of the asset if she cashed out - she would have only paid taxes on the net gain in value."
Shares held in a retirement account are not subject to capital-gains treatment. When distributed from the retirement account, the value distributed is taxable according to the tax treatment on distributions from that type of retirement account, the same treatment regardless of the type of asset. The taxable amount is taxable as ordinary income.
"This is not a typical "distribution" from a retirement plan in the traditional sense."
If it was reported on a Form 1099-R, it is a distribution from a retirement account and is taxable as such.
The annual gift-tax exclusion has nothing to do with this. This was not a gift.
If you (not the trust) were the recipient of the Form 1099-R, what apparently happened is that the trust transferred your share of the IRA inherited by the trust to an inherited IRA for your benefit and you then took a distribution from the inherited IRA maintained for your benefit.
