Learn Hardcore German: Meine Schwiegermutter bleibt heute zu Hause, weil sie müde ist. - My mother-in-law is staying at home today because she is tired.

Schwieger- is a prefix used in family words to mean “-in-law” (like Schwiegervater = father-in-law, Schwiegersohn = son-in-law).
Mutter means mother.

German often combines words into a single long noun like this; only the whole compound’s first letter is capitalized: Schwiegermutter.

Why is it bleibt and not just ist (why “stays at home” and not “is at home”)?

Bleiben means to stay / remain, while sein means to be.

Meine Schwiegermutter bleibt heute zu Hause = She stays/remains at home today (she is not going out as she might otherwise do).
Meine Schwiegermutter ist heute zu Hause = She is at home today (just describing her location, no emphasis on staying).

In your sentence, bleibt suggests a decision or situation of not going out because she is tired.

What’s the difference between zu Hause, nach Hause, and im Haus?

They express different ideas:

zu Hause = at home (state/location)
- Sie ist zu Hause. – She is at home.
nach Hause = (to) home (direction, going home)
- Sie geht nach Hause. – She is going home.
im Haus = in the house / inside the building (physically in a house, not necessarily your own home)
- Sie ist im Haus. – She is in the house (not outside).

In your sentence, zu Hause is used because it’s about staying at home (location).

Why is it zu Hause with Hause, not zu Haus or zu dem Haus?

Zu Hause is a fixed expression meaning at home.

Hause is an old dative form of Haus, preserved only in certain set phrases: zu Hause, nach Hause.
Modern standard German normally uses zu Hause and nach Hause for at home / (to) home.
You might also see zuhaus(e) in informal writing, but zu Hause is the safest, most correct form.

Zu dem Haus would mean to the house (to that specific building), not at home.

Why is there a comma before weil, and what happens to the word order after weil?

Weil introduces a subordinate clause (a dependent clause expressing the reason: because she is tired). In German:

You must put a comma before most subordinate conjunctions, including weil.
In a weil-clause, the conjugated verb goes to the end of the clause.

So:

..., weil sie müde ist. (literally: because she tired is)

If it were a main clause, the verb would be in second position:

Sie ist müde. – She is tired.

Could I use denn instead of weil, and what would change?

Yes, you could say:

Meine Schwiegermutter bleibt heute zu Hause, denn sie ist müde.

Differences:

weil introduces a subordinate clause → verb goes to the end: weil sie müde ist.
denn introduces a coordinating clause → normal main-clause word order: denn sie ist müde.

In meaning, both give a reason (because / for). In everyday speech, weil is more common and slightly more informal; denn sounds a bit more written or explanatory.

Why is it weil sie müde ist and not weil sie ist müde?

After weil (and other subordinating conjunctions like dass, wenn, obwohl), German grammar requires that the finite (conjugated) verb stands at the end of the clause.

So:

Correct: weil sie müde ist.
Incorrect: weil sie ist müde.

In English, the word order doesn’t change after because, but in German it must: Subordinate clause = (subject + rest + verb at the end).

How do I know that sie here means she, and not they or formal you?

German sie/Sie can mean she, they, or formal you, depending on capitalization and context:

sie (lowercase, singular feminine) = she
sie (lowercase, plural) = they
Sie (capital S) = formal you (singular or plural)

In your sentence:

It refers back to meine Schwiegermutter (a singular feminine person).
It is written lowercase sie. So it must mean she: weil sie müde ist = because she is tired.

Why doesn’t müde change its ending to agree with sie? Should it be müde or something like müden?

Predicate adjectives in German (adjectives after sein, werden, bleiben, etc.) do not take endings. They stay in their basic form, regardless of gender, number, or case.

So you always say:

Sie ist müde.
Er ist müde.
Wir sind müde.
Die Kinder sind müde.

No endings: müde stays müde in all of these.

Where can I put heute in this sentence, and does the position change the meaning?

Heute (today) is a time adverb and has flexible position. All of these are correct:

Meine Schwiegermutter bleibt heute zu Hause, weil sie müde ist.
Heute bleibt meine Schwiegermutter zu Hause, weil sie müde ist.
Meine Schwiegermutter bleibt zu Hause heute, weil sie müde ist. (possible, but less natural)

Native speakers most often put heute early in the sentence: either right after the verb or at the very beginning. The basic meaning doesn’t change; moving heute slightly shifts emphasis.

Why is the verb bleibt in second position, even though there are several words before and after it?

In main clauses, German normally follows the V2 (verb-second) rule: the conjugated verb must be the second element of the clause.

In Meine Schwiegermutter bleibt heute zu Hause:

Meine Schwiegermutter = first element (the subject, as one block)
bleibt = second element (the verb)
heute zu Hause = everything else after the verb

Even if you move parts around, the finite verb still stays second:

Heute bleibt meine Schwiegermutter zu Hause.
Zu Hause bleibt meine Schwiegermutter heute.

Is the tense here strictly present, or can bleibt also refer to the future?

Grammatically, bleibt is present tense. However, German present tense often covers situations that in English would use the future:

Meine Schwiegermutter bleibt heute zu Hause can be:
- My mother-in-law is staying at home today.
- My mother-in-law will stay at home today. (if you’re talking about a plan)

You only need a clear future form (wird bleiben) when you want to strongly emphasize futurity or make the timing very explicit, but in everyday speech, the simple present is usually enough.