Phrase for a child moving around -- "ritching around"?

Solution 1:

I live in PA, and it's a very common word among the PA Dutch (I've picked up a great many strange words and expressions from them.)

It's not quite "ritching"; the first syllable's vowel sound is more like the oo in book. So I would spell it "rootching", but, yes. It is equivalent to squirming:

a change of position that does not entail a change of location -TFD

Synonymous with fidgeting, wiggling, etc.

Solution 2:

Ritching around was used in my family too! By my grandmother whose mom came from Bavaria. German roots maybe? Yes. I found the German word rutsch which can be used to mean stop sliding (rutsching) your bum around.