If you have decided to realise the investments, it is better to sell them off in India due to the lower rate of tax, as compared to Ireland (In Ireland, tax on capital gain arising on sale of certain specified foreign investment products is 40%).
For LTCG on US listed stocks, tax rate would be 20% with indexation [there is no option available to claim 10% without indexation in your case]
For LTCG on Indian listed stocks, tax rate would be 10% (post Rs. 1 lakh).
You need not transfer the money to your parents account. You can directly remit the money from your own account and that would not be taxable in Ireland.
Alternatively, if you do not want to sell the shares right now, you may gift the shares to your parents before you move to ireland - There would be no tax implication on account of such gifting. Subsequently, whenever you want money to be remitted to you in Ireland, your parents may sell off the shares and remit the money to you by way of gift, in chunks of €3000 per year. At the time of sale, the taxation in the hands of your parents will be the same as mentioned above.
There can be other alternatives as well, depending upon your exact requirement.