Learn Hardcore Japanese: sono gaka ha sainou ga aru dake de naku, kodomotati ni e wo osieru kunren mo ukete iru sou desu. - I hear that that painter not only has talent, but has also received training in teaching art to children.

その画家は – topic of the sentence (what we’re talking about): “As for that painter…”
才能がある – a fact about the topic:
- 才能 = talent
- が marks 才能 as the grammatical subject of ある
- ある = to exist / to have (for inanimate things or abstract qualities)

So literally:

その画家は才能がある = “As for that painter, (he) has talent.”

Using は for the person and が for the quality they possess is very natural in Japanese.

What is the role of も in 訓練も受けている? Can it be left out?

も means “also / too / as well.”

Because the first part says the painter has talent, the second part says they also have another good point: they have received training.

訓練を受けている = is/has been trained, has received training
訓練も受けている = has also received training

If you remove も:

訓練を受けている is still grammatical and understandable.
But you lose the clear “in addition to the talent just mentioned” nuance. The も ties the second point to the first as another positive feature.

Why is it 子供たちに絵を教える and not 子供たちを絵を教える?

With 教える (“to teach”), Japanese usually uses:

X に Y を教える = “teach Y to X”
- X = person being taught → takes に
- Y = thing being taught → takes を

So:

子供たちに = to the children (indirect object)
絵を = (how to) draw/paint pictures (direct object)
子供たちに絵を教える = “teach drawing/painting to children”

Using 子供たちを絵を教える is wrong because を there would mark 子供たち as the direct object (the thing being taught), which doesn’t make sense.

Is 絵を教える訓練 a kind of relative clause? How should I understand this structure?

Yes, it is basically like a relative clause in English.

Structure:

絵を教える = (to) teach drawing/painting
訓練 = training

In Japanese, a verb phrase can directly modify a noun before it:

絵を教える訓練 ≈ “training (for) teaching drawing/painting”
- more natural English: “training in how to teach children drawing/painting”

So the whole part 子供たちに絵を教える訓練 is:

訓練 (training)
specified by 子供たちに絵を教える (teaching drawing/painting to children)

= “training to teach drawing/painting to children.”

What nuance does 受けている have here? Is it “is receiving” or “has received”?

受けている is 受ける in the ～ている form.

受ける (here) = to receive, to undergo (e.g., training, lessons, surgery)
～ている can mean:
- an ongoing action (is doing), or
- a resulting state from a completed action (has done and is now in that state)

With 訓練を受けている, the most natural reading is:

Resulting state: the person has undergone training and is now someone who has that training.

So in natural English, you’d usually say:

“has received training” or “has been trained”, not “is receiving training” (unless context clearly stresses that it is happening right now).

What does そうです mean here? Is it “I heard” or “it seems”?

そうです has two common uses:

Hearsay: “I hear that … / They say that …”
Appearance / conjecture: “It seems … / It looks …”

Which one is it here?

The sentence before そうです is in plain form:
受けているそうです
In that pattern, V-plain + そうです usually expresses hearsay.

So here:

受けているそうです ≈ “I hear (that) he has received training” / “It’s said that he has received training.”

If it were appearance/conjecture (“seems”), you’d typically see a different form like:

受けていそうです or other context clues.

What’s the difference between だけでなく and だけではなく? Are both correct?

Both だけでなく and だけではなく are grammatically correct and very common.

だけでなく
だけではなく

In everyday conversation, では is often shortened to で, so:

だけではなく → だけでなく

Nuance:

Any difference in nuance is very small; in most contexts, they are interchangeable.
Some people feel だけではなく can sound a bit more explicit/emphatic, but this is subtle.

So you could also say:

その画家は才能があるだけではなく、子供たちに絵を教える訓練も受けているそうです。

Meaning is essentially the same.

Why その画家 and not あの画家? What is the difference?

Both その and あの mean roughly “that”, but the nuance is:

その: “that (one you know / that we’ve been talking about / that is near you or contextually known)”
あの: “that over there / that one (not near either of us, or not in our immediate shared context)”

In practice:

その画家: “that painter (that you know / we both know from context or a previous mention)”
あの画家: “that painter over there” / “that painter (distant or not directly in our shared context)”

In many textbook examples, その is used when referring to someone already introduced or understood in the conversation, which is probably the idea here.

Could you break down the sentence word by word so I can see the structure more clearly?

Sure.

その – that (demonstrative)
画家 – painter, artist (specifically in painting)
は – topic marker (“as for …”)

才能 – talent
が – subject marker
ある – to exist / to have

だけでなく、 – not only (that) but also

子供たち – children
に – to (indirect object marker, person being taught)

絵 – pictures / drawings / painting
を – direct object marker

教える – to teach

訓練 – training

も – also, too

受けている – is in the state of having received / has received (training)

そうです。 – it is said / I hear that (hearsay)

Putting it together structurally:

[その画家は]
[才能がある] だけでなく、
[子供たちに絵を教える訓練も受けている] そうです。

= “As for that painter, (he) not only has talent, but I hear (he) has also received training to teach children drawing/painting.”