一、根据所查到的例句和张克礼《新英语语法》的相关说明，下面两句都对，意思也差不多，不同的只是结构（有for时用there to be；没有for时用there being）：

1. There being a swimming pool in our school is what we expect.

2. For there to be a swimming pool in our school is what we expect.

二、用作主语补语（表语）时，根据张克礼《新英语语法》的相关说明，只能用for there to be：

误：What we expect is there being a swimming pool in our school.

正：What we expect is for there to be a swimming pool in our school.

附张克礼《新英语语法》的相关截图：

【一】There being a swimming pool in our school is what we expect.【动名词复合结构作主语】

【备注(1):There being a swimming pool in our school为动名词复合结构整体作句子主语】

【备注(2):there 为being形式逻辑主语，a swimming pool为being真正逻辑主语】

【备注(3):what we expect 为融合型关系代词what=the thing that 引导名词型关系分句，并在主句作表语，构成表语从句,what we expect=the thing that we expect】

There being a swimming pool in our school is what we expect.【动名词复合结构作主语】

=That there is a swimming pool in our school is what we expect.【that主语从句作主句的主语，what表语从句作主句的表语】
=That there is a swimming pool in our school is the thing that we expect.

=It is the thing that we expect that there is a swimming pool in our school.

There being a swimming pool in our school 【主语】// is 【系动词】// what we expect 【表语】//.

参考译文：学校拥有一个游泳池是我们所期望的事情。

【二】What we expect is for there to be a swimming pool in our school.【不定式复合结构作表语】

【备注(1):for there to be a swimming pool in our school 为不定式复合结构整体作句子表语】

【备注(2):there 为to be形式逻辑主语，a swimming pool为being真正逻辑主语】

What we expect【主语】//  is【系动词】//  for there to be a swimming pool in our school【表语】// .

参考译文：我们所期望的事情是学校拥有一个游泳池。

【三】For there to be a swimming pool in our school is what we expect.【不定式复合结构作主语】

【备注(1):for there to be a swimming pool in our school为不定式复合结构整体作句子主语】

【备注(2):there 为to be形式逻辑主语，a swimming pool为being真正逻辑主语】

For there to be a swimming pool in our school 【主语】// is 【系动词】// what we expect 【表语】//.

参考译文：学校拥有一个游泳池是我们所期望的事情。

【四】What we expect is there being a swimming pool in our school.【动名词复合结构作表语】

【备注(1): there being a swimming pool in our school 为动名词复合结构整体作句子表语】

【备注(2):there 为being形式逻辑主语，a swimming pool为being真正逻辑主语】

What we expect【主语】//  is【系动词】//  for there being a swimming pool in our school【表语】// .

参考译文：我们所期望的事情是学校拥有一个游泳池。

特别备注：

【1】不定式复合结构for there to be a swimming poor作主语或者表语表示“将来拥有一个游泳池”。

【2】动名词复合结构there being a swimming poor作主语或者表语表示“已经拥有了一个游泳池”。