Do I have this correct?

[jannie]

If I have the mtdna test, it may show connections for my mother - mother's line? (But, I'm not really interest in that line.)
However, there is another line I'm interested in.
1. My father's grandmother -- My GreatGrandmother - She died shortly after arriving here from Germany with her 3 young children (2 boys 1 girl). The girl married and had children - if she had a female child would that childs female children be the carrier of the mtdna that may tell me some info about the mother?

[LynCra]

Yes, her female descendants should be able to help you to find out more about her through mtdna testing. But be aware that there can be some changes. As an example, I have a one step difference from my maternal aunt, so something has changed either between my mother and I or between my maternal grandmother and two of her daughters.

[prairielad]

your fathers Grandmothers mtdna is passed on to
-all her children, male and female (your fathers aunts and uncles)
-her daughters passed it on to all their children, Male and female (all your fathers 1st cousins who are children of your fathers aunts)
-all of your fathers female 1st cousin's children, male and female.

So to answer part of your question

all of that childs children, male and female, will be carriers of your Great Grandmothers mtdna.

Edit: if this is your father's maternal Grandmother, he also will be a carrier of this mtDNA.

[jannie]

Thank you. I have found a gggrandson of my grandfathers sister I guess that makes sense. So if he took the mtdna test this may offer some insight.?

[prairielad]

providing this gggrandson maternal line follows all females back to your Great Grandmother in question, then yes he will have her mtDNA.

Keep in mind mtDNA is more for a deeper understanding of this lines deeper ancestry.

https://www.familytreedna.com/learn/...-relationship/