W nowej łazience stoi duża wanna, więc dzieci będą miały więcej miejsca.

Because the preposition w meaning in requires the locative case when it answers the question where?

So:

• łazienka = bathroom
• w łazience = in the bathroom

The adjective must match the noun, so:

• nowa łazienka = a new bathroom
• w nowej łazience = in the new bathroom

Both words change because Polish adjectives and nouns have to agree in case, gender, and number.

In Polish, stać often means that an object is standing / positioned / located upright somewhere. It is very commonly used for furniture and large objects.

So:

• W kuchni stoi stół = There is a table in the kitchen / A table stands in the kitchen
• W łazience stoi wanna = There is a bathtub in the bathroom

In natural English, we usually say there is rather than stands, but in Polish stać is very normal here.

Duża wanna is in the nominative case because it is the grammatical subject of the sentence.

• duża = big / large
• wanna = bathtub

Together: duża wanna = a large bathtub

Even though it comes after the verb stoi, it is still the subject. Polish word order is flexible, so the subject does not always have to come first.

Polish word order is flexible, and different orders give different emphasis.

• W nowej łazience stoi duża wanna puts emphasis on where the bathtub is.
• Duża wanna stoi w nowej łazience is also correct, but sounds a bit more neutral or puts more attention on the bathtub itself.

Starting with the location is very natural in Polish when introducing what is in a place.

Więc means so, therefore, or thus.

It connects the two parts of the sentence:

• there is a large bathtub in the new bathroom,
• so the children will have more space.

It is a very common linking word in Polish. In speech, it can also sound a little conversational, just like so in English.

This is the future tense of mieć (to have).

Polish forms the future of imperfective verbs with:

• będę / będziesz / będzie / będziemy / będziecie / będą
• plus the past-like form of the main verb

Here:

• dzieci = children
• będą miały = will have

So literally it is something like children will had, but in real grammar this is just the standard Polish future construction for mieć.

Because dzieci is treated grammatically as non-masculine-personal plural.

In Polish plural past and future forms, there is an important distinction:

• mieli = masculine-personal plural, used for groups of men or mixed groups treated as masculine-personal
• miały = non-masculine-personal plural, used for things, animals, and many groups not treated as masculine-personal

Although children are people, the noun dzieci takes the non-masculine-personal form in this pattern:

• Dzieci były zmęczone
• Dzieci miały czas
• Dzieci będą miały miejsce

So miały is correct.

After words like więcej (more), Polish usually uses the genitive case.

So:

• miejsce = place / space
• miejsca = genitive singular

That is why:

• więcej miejsca = more space

This is a very common pattern:

• więcej czasu = more time
• więcej pieniędzy = more money
• więcej wody = more water

In this sentence, miejsce is best understood as space.

So dzieci będą miały więcej miejsca means the children will have more room to move around.

Polish miejsce can mean:

• place in many contexts
• space / room in others

Here, because we are talking about a bathroom with a large bathtub, more space is the natural meaning.

You could, but it would sound less natural in this context.

• W nowej łazience jest duża wanna = There is a large bathtub in the new bathroom
• W nowej łazience stoi duża wanna = A large bathtub stands/is positioned in the new bathroom

Both are understandable, but stoi is especially natural for furniture and large objects that occupy space in a room. It gives a more concrete image.

Dzieci is plural. It is the plural of dziecko (child).

• dziecko = child
• dzieci = children

It is an irregular plural, so you just have to learn it as a whole form.

In the sentence, dzieci is in the nominative plural, because it is the subject of będą miały.

Yes. Wanna is the standard everyday Polish word for bathtub.

Examples:

• Mam wannę w łazience. = I have a bathtub in the bathroom.
• To jest duża wanna. = This is a large bathtub.

Just be aware that wanna has a double n. It is a normal Polish noun, feminine in gender.

Polish does not have articles like English a and the.

So:

• duża wanna can mean a large bathtub or the large bathtub
• dzieci can mean children or the children

You understand the difference from context. In this sentence, English naturally uses a large bathtub and the children, but Polish does not need separate article words.