What is the name of this "yawning like" movement?

Solution 1:

There is a specific name for it: pandiculation.

A stretching and stiffening of the trunk and extremities, as when fatigued and drowsy or on waking, often accompanied by yawning.

http://en.wiktionary.org/wiki/pandiculation

_{Joseph Ducreux pandiculating; self-portrait ca 1783}

Note: While stretching is more common, it is also more general. OP didn't specifically asked for a common word and there are details in the question. Pandiculation is a tailor-made word for this specific movement. At least, you learned a new word if you didn't know it.

Solution 2:

She is doing the same thing this cat is doing: stretching.

English doesn't have a common word for the stretching associated with yawning, or with waking up. Do it whenever you need to, just because it feels good.

Solution 3:

Rax

(Britain, dialectal, chiefly Scotland, intransitive) To stretch after sleep.