1. I demanded that he should give me the money.
2. I suggested that we should go on a picnic tomorrow.
3. He insisted that she should join the club.
4. I demanded that he give me the money.
5. I suggested that we go on a picnic tomorrow.
6. He insisted that she join the club.
( Are they all grammatical? The other three sentences don't have 'should.')
The sentences without "should" are fine. Adding the word "should" is unneeded since these sentences include subjunctive clauses anyway.
Yes, all the sentences you provided are grammatical. However, there is a difference in the construction of sentences 1 to 3 compared to sentences 4 to 6.
Sentences 1 to 3 use the construction "should + base form of the verb" after the verbs "demand," "suggest," and "insist." This construction indicates a stronger or more forceful request or recommendation. It implies that the speaker believes the action or outcome is necessary or required.
Example:
1. I demanded that he should give me the money. (Strong and forceful request)
2. I suggested that we should go on a picnic tomorrow. (Strong recommendation)
3. He insisted that she should join the club. (Strong belief that it is necessary)
On the other hand, sentences 4 to 6 omit "should" and use the base form of the verb after the same verbs. This construction still conveys the request, suggestion, or insistence, but it does not emphasize the level of necessity as strongly as when "should" is included.
Example:
4. I demanded that he give me the money. (Request without strong emphasis on necessity)
5. I suggested that we go on a picnic tomorrow. (Suggestion without strong emphasis on recommendation)
6. He insisted that she join the club. (Insistence without strong emphasis on necessity)
So, all the sentences are grammatical, but there is a difference in the level of force or emphasis conveyed based on the inclusion or omission of "should" in each sentence.