Breaking the offending sentence into two sentences is grammatically correct but often rhythmically wrong.
Or it may be the head only that is rhythmically moved from side to side, and the performance may go on indefinitely.
There was a colour in the chaplain's cheek and he swayed ever so slightly and rhythmically in his saddle.
Repeat this rhythmically many times, sustaining as far as possible the expansion of the chest.
Zollern tapped his cane on the parquet floor, rhythmically, persistently.
The amnion in fact begins to pulsate slowly and rhythmically, and by its pulsation the embryo is rocked to and fro in the egg.
“The more you give way, the more give you may,” said Mrs Purkis, rhythmically.
Consciousness is rhythmically disposed, because the whole organism is rhythmically disposed.
The sound of our merriment mixing so rhythmically was music to my ears.
When the coil is set to work, the molecules of the air are rhythmically attracted and repelled.