How are 我们把那张画儿挂上去吧。and 我们挂上去那幅画吧。 different?
[1. 我们] [2. 挂] [3. 上去] [4. 那幅画] [5. 吧]
[1. subject] [2. verb] [3. directional (verb) complement] [4. object] [5. final particle]

The problem here is, in Chinese grammar, the object should be inserted between the 'verb' and the 'directional complement'
The following is the correct structure:

[1. 我们] [2. 挂] [3. 那幅画] [4. 上去] [5. 吧]
[1. subject] [2. verb] [3. object] [4. directional (verb) complement] [5. final particle]

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why 我们挂上去那幅画吧。with 上去 is not acceptable, but, if I leave out the 去， 我们挂上那幅画吧。is acceptable. How are they different?

The reason why &quot;我们挂上去那幅画吧&quot; is not acceptable has been explained above.

&quot;我们挂上那幅画吧&quot; is not technically incorrect, but the meaning is ambitious. Since the indirect object is omitted, it could mean &quot;我们(在身上)挂上那幅画吧&quot; or &quot;我们(在墙上)挂上那幅画吧&quot;

In summary:

Both &quot;我们把那张画儿挂上去吧&quot; and &quot;我们挂那幅画上去吧&quot; are clear and correct

我们挂上去那幅画吧 is grammatically incorrect

我们挂上那幅画吧  is too ambitious, it needs an indirect object

我们挂那幅画吧 actually removed the ambiguity, because '挂上' is equally applicable for 'on person' and 'on the wall', while '挂' strongly implied  'to hang (on the wall)'


Example of [verb]+ [direct object] +[indirect object]

In &quot; I give you a toy&quot;,  'you' is the indirect object, and 'toy' is the direct object
similarly, in &quot;我们(在墙上)挂上那幅画吧&quot;, '那幅画' is the direct object, '墙'is the indirect object