What is рученюсенька?

It’s definitely a constructed (though grammatically correct) word meaning a very-very-very small and cute hand/arm. Possibly you could say it to a small child. Never would expect to hear it in everyday situations.

If there was such a word in Russian, it would mean “a small lovely child’s hand”.

lil lovely hand

There are 4 diminutive suffixes that can be applied to a word рука: ручка, ручечка, рученька и ручонка. In this case it’s some artificial combination of them all, something like “itsy-bitsy teenie-weenie hand”