My understanding is that a Discretionary Discounted Gift Trust is a normal relevant-property discretionary trust - the only difference being that because your late mother, the settlor, received guaranteed payments of capital in her lifetime the initial transfer to the trust is "discounted" for IHT purposes. The calculation of the discount is complex and would have been agreed with HMRC.
Once payments to your mother have ceased, the trust is just a discretionary trust holding assets - usually a non-income producing investment bond (onshore or offshore) - for a class of beneficiary. In order to wind up the trust, you, the trustee, need to check what the original settlement says with regards to appointment of the capital. Usually it will require a formal Deed in order to appoint capital to the beneficiaries.
The investment bonds and life insurance policies etc used for these trusts fall into the "chargeable event" regime, so tax is not payable during the normal lifetime of the bond but only at certain "chargeable events" e.g surrendering the bond, taking more than 5% out of it etc. You can normally transfer a bond or part of it to another person without triggering a chargeable event. The new owner holds the bond as if they have always had it and is only taxed when there is a chargeable event.
So I believe, once you have checked how the trust appoints capital, units of the bond can be transferred to the beneficiaries without CGT or income tax on either the trust or them. Until they surrender it of course, they they pay income tax. (Alternatively, the trust can surrender the bond and distribute the cash with no tax on the beneficiaries - but usually this is not advantageous as the trust pays higher tax rates.)
However, because this is a relevant-property trust, the transfer is subject to the IHT Exit Charge - if the assets are less than the IHT threshold it may be 0. If you paid IHT at a 10 year review it will be some proportion of that. Its complex and depends on lots of other things...
You can find some more detail info here
https://techzone.abrdn.com/public/iht-e ... unted-gift