"it so happens my custodian has told me today I do not have to pay the 10% penalty from my own fund, rather, they will handle that."
If you roll over the entire gross amount, there is no penalty. I can't imagine what they are going to "handle." All they need to do is accept the rollover of whatever amount gets deposited into the traditional IRA as a rollover contribution.
When entering the Form 1099-R into TurboTax, you will tell TurboTax the amount that was (will be) rolled over and TurboTax will exclude this amount from the amount of taxable income shown on Form 1040 line 4b and will mark the box to indicate a rollover.
I'm now quite confused about what the mistaken transaction was and the type of account from which the distribution was made. If there was an in-kind distribution of shares from a Roth IRA, there would have been no cash to withhold for taxes. If the distribution was instead a cash distribution, there would have been no capital gains. Only if there was a distribution of a combination of cash and shares could you have both tax withholding and capital gains.
If there was an in-kind distribution was from a Roth IRA, you are not permitted to sell the shares and roll over the proceeds. Only if the distribution was from a designated Roth account in an employer plan are you permitted to do that.
What is the code in box 7 of the Form 1099-R?
Is the IRA/SEP/SIMPLE box marked?
