Can´t kendisi refer to the subject, the beater?

"Kendisi tembel olduğu için çocuğu dövdü"

Kendisi in this sentence refers to the subject. Here the beater is tembel.

"Tembel olduğu için çocuğu dövdü"

In this sentence the child is tembel.

Let´s simplify the sentence:

(O)--------çocuğu--------dövdü 

subject ---object---------verb

Tembel olduğu için is adverb complement (answers the question why/for what) and you can place it either before or after the object in this sentence:

Tembel olduğu için çocuğu dövdü

Çocuğu tembel olduğu için dövdü

Instead of "olduğu için" use "diye", it is easier and causes no ambiguity. 

Ucuz diye elma aldım.

Tembel diye çocuğu dövdü.

This diye-structure is interesting. I didn´t pay attention to it but recently. It seems to me a handy way to lighten the stream of complicated participle structures which Turkish is quite well provided with.

I still didn´t really shake hands with kendi. It doesn´t (quite) fit any scheme that I have got used to in other languages. Is it that is generally refers to the subject of the main clause if there is one or is this a simplification? Usually it makes things more complicated to me. I guess it will just take some time and more material to get used to it.

Ambiguity has caused a lot of problems to me recently when trying to learn Turkish and I see now that it´s partly because the sentences which I look at are separated from their environment. Trying to make them waterproof in these circumstances may cause problems. Maybe I should be more worried about if they are grammatical or not.

It would be a shame not to learn with all this help that I´m getting. Thank you, si++, scalpel.

Turkish is ambiguous.

One source of confusion is because of pronomial-n.

Evini may be ev-i-n-i (house+3rd sg. poss+pro-n +acc) or ev-in-i (house + 2nd sg poss + acc)

Evine may be evi-n-e (house+3rd sg. poss+pro-n +dat) or evin-e (house + 2nd sg poss + dat)

Adjective may be used or nouns or adverbs sometimes may be another source of confusion.

Consider the following sentence:

Küçük kırmızı topa vurdu.

With no punctuation and context it is 3 way ambiguous (Can you see how?)

Is it that the subject can be either sg 3rd, küçük or küçük kırmızı?

yes and one more

Küçük, kırmızı topa vurdu. (The little one hit the red ball.)

Küçük kırmızı, topa vurdu. (The little red (one) hit the ball.)

Küçük kırmızı topa vurdu. (He hit the little red ball.)

See, the problem is that you don´t mark everything. If you conjugated your adjectives also like they do in certain languages no such problems would occur.

You mean like in Italian (or Russian/etc.) where they modify adjectives for number and gender? That is another detail which complicates the matters and makes the things difficult to learn IMHO. Turkish evolved for simplicity over centuries.

In reality this is no big problem for us. You have always a context and can see the real meaning.