Inheriting twice

Yes they will. The procedure is set out in S.98 of the Succession Act, copied and pasted below. In your case, the estate will be divided as if you survived your father but died immediately after him. The will could be worded to deal with your death in advance of his but if it's as you outlined with no alternative procedure if you predeceased him, your estate will inherit your one third and your children will get their share of the bequest to the grandchildren.

So if you and your brother have two children each and you died before your father, your two children would get one-sixth each (your one-third split two ways) from your bequest plus one-twelfth each (one-third split four ways) from the grandchildren bequest. Which means they would get one-quarter of the estate each. Your brother would get one-third and his two children would get one-twelfth each.

You talk about your bequest going direct to your children but if your wife is alive, she would have a claim on some of the money.

98.—Where a person, being a child or other issue of the testator to whom any property is given (whether by a devise or bequest or by the exercise by will of any power of appointment, and whether as a gift to that person as an individual or as a member of a class) for any estate or interest not determinable at or before the death of that person, dies in the lifetime of the testator leaving issue, and any such issue of that person is living at the time of the death of the testator, the gift shall not lapse, but shall take effect as if the death of that person had happened immediately after the death of the testator, unless a contrary intention appears from the will.

https://www.irishstatutebook.ie/eli/1965/act/27/section/98/enacted/en/html#sec98

OP mentioned 'my kids' so S.98 applies.