I think it's a bit weird as well. But, at least, your DD was named first, so she's the first [Jenny/Jennifer] in the family. KWIM?
A little story...
Our DD is named my most favorite female name ever. I wanted to use the name if I ever had a little girl for forever... years before I was even pregnant.
It's a name that is commonly shortened - like Jenny/Jennifer.
Well, 3 years before DH & I had our DD, my SIL (DH's brother wife) was pregnant w/ her 3rd child. At her first ultrasound, they were told they were having a girl. And then my SIL said they had decided to name the baby w/ the shortened form of my favorite name.
I was heartbroken because I knew then that I wouldn't be able to name our little girl w/ the long form of the same name - if we even had a little girl.
I just felt like there couldn't be first cousins w/ the same name - long or short versions.
Well, surprise! My SIL ended up having a boy.
So, 3 years later, when we had our DD, I was able to use "my" name.
Likewise, for our 2nd DS, I really, really liked the name of one of my nephews, but we didn't use it... since it had already been used.
In larger families, I know it's not that uncommon for the same names to be used over the years, especially as the family expands. And, many times, cousins will share the middle names.
However, I don't think you normally hear of 1st cousins w/ the same first names that often - especially when the families/cousins are together & see other frequently.