I put Dutch Girl in the DT, with the motions, quite a long time ago:

I AM A PRETTY LITTLE DUTCH GIRL

I am a pretty little Dutch girl
As pretty as pretty can be
And all the boys around my way
Go crazy over me

My boyfriend's name was fatty
He comes from Cincinnati
With a pimple on his nose
And three black toes
And this is how my story goes

...

This was a clapping game in Brooklyn in the '50s
The motions were as follows:
two girls sat facing each other within clapping distance
clap self, clap right hands, clap self, clap left hands,
clap both hands with other, hands on own shoulders,
clap on own knees, repeat.
There are more verses
@kids
filename[ DUTCHGRL
SOF

I don't know the shop verse Azizi quoted, but do know the rest, but

One day when I was walking,
I saw my true love talking,
To a pretty little girl
With a strawberry curl,
And this is what he said:
I L-O-V-E love you
All the T-I-M-E time,
And I'll K-I-S-S kiss you
Tomorrow night at nine.

Lulu had a Steamboat is also in the DT, along with some other "teaser somes", but they did not have motions, nor were used for jumprope or ball.

A my name is Alice was a ball bouncing rhyme and I think the ball went under the leg at the last word of the line.

I don't remember what we did with:
Oh they don't wear pants
On the other side of France
But they do wear grass
Just to cover up their ass...

We did ball bouncing to:
I saw London, I saw France
I saw ________'s underpants
Are they white? Are they pink?
I don't know, but they sure stink

Brooklyn in the 1950s
Azizi - I looked up your profile - we are almost exactly the same age. I don't know why I thought you were younger.