Assalaamu alaikum wa Rahmatullah
We most of Bangladeshis wear pants over shirts in offices. So the shape of our waists (below the navel) becomes visible to others. Particularly when we bow and prostrate in Salah, the shape of our backs and private parts become clear to others. In such a case, performing salah with these dresses would be correct or not?
I personally changed the pants-shirt, and started wearing Panjabi pajamas. But my wife is dead against my decision. Even she tells me she will leave my house. What should I do? I earnestly request you to answer this as soon as possible.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, is His slave and Messenger.

If you mean that the skin of the ‘Awrah is visible, then the prayer is invalid. However, if you mean that the skin is not visible, but the garment is tight-fitting, outlining the size of the ‘Awrah, then the prayer is valid, yet praying in this state is disliked. Ibn Qudaamah said in Al-Mughni:

It is obligatory to cover the ‘Awrah with what conceals the color of the skin. If the garment is see-through and shows the color of the skin underneath it, revealing whether it is white or red, then it is invalid to pray while wearing it, because this does not fulfill the required covering of the 'Awrah. If it obscures the color of the skin but it [is tight-fitting and] outlines the shape of the ‘Awrah, then the prayer is valid because this cannot be avoided, even with a thick garment. [End of Quote]

Ash-Shaafi‘i stated that it is disliked to pray in tight clothes, and stated that this is more emphasized for a woman. He said: “If he performs the prayer in a transparent Qamees (long Islamic-style shirt-Thawb), showing the ‘Awrah underneath it, the prayer is invalid (in terms of clearing his liability from the obligation) … If he performs the prayer in a single Qamees that (is tight-fitting and) outlines his shape but is not transparent, I would dislike it (deem that his prayer is disliked). However, it is not evidently proven that he is obliged to repeat the prayer.” [End of Quote, summarized] This applies to women with greater reason.

Your wife does not have the right to object to what you are permitted to wear as per the Sharee‘ah, let alone threatening you to leave the house. This is considered Nushooz (rebellious behavior) on her part; it is obligatory on her to fear Allah, The Almighty, and beware of exaggeration.

For more benefit, please refer to Fatwa 297154.

Allah knows best.