Vor dem Spaziergang wickelt meine Schwester ihre Tochter und packt danach die Wickeltasche.

German often puts time expressions at the beginning of a sentence to set the scene.

So:

Vor dem Spaziergang wickelt meine Schwester ihre Tochter ...
= Before the walk, my sister changes her daughter ...

This is very natural in German. When a time phrase comes first, the conjugated verb still has to stay in second position, which is why you get:

• Vor dem Spaziergang = position 1
• wickelt = position 2

You could also say:

Meine Schwester wickelt vor dem Spaziergang ihre Tochter ...

That is also correct, just with a different emphasis.

Because vor here is followed by the dative case.

Vor is a two-way preposition, but in a time expression like this, it takes the dative:

• vor dem Spaziergang = before the walk

Spaziergang is masculine, so in the dative singular:

• der Spaziergang → dem Spaziergang

So this is not about movement; it is simply a time phrase.

Here wickeln means to change a baby's diaper/nappy.

Literally, wickeln can mean to wrap or to swaddle, but in everyday family context, when someone wickelt ein Baby / ein Kind, it usually means to change the child’s diaper.

So:

• ein Kind wickeln = to change a child’s diaper

This is a very common parenting verb in German.

By itself, ihre can sometimes mean her or their, depending on context. But here the context makes it clear:

meine Schwester = my sister

So:

ihre Tochter here naturally means her daughter, referring to my sister’s daughter.

German does not change the possessive form here just because it refers back to the subject. English learners sometimes expect something special like a reflexive possessive, but German simply uses the normal possessive:

• meine Schwester ... ihre Tochter = my sister ... her daughter

Yes. Ihre Tochter is the direct object of wickelt.

The structure is:

• meine Schwester = subject
• wickelt = verb
• ihre Tochter = direct object

So the daughter is the person receiving the action.

It may not look different from the nominative because feminine singular often has the same form in nominative and accusative:

• nominative: ihre Tochter
• accusative: ihre Tochter

So the case is accusative, even though the form does not change visibly here.

Because German often omits a repeated subject in coordinated clauses when it is the same as in the first clause.

So:

Vor dem Spaziergang wickelt meine Schwester ihre Tochter und packt danach die Wickeltasche.

means:

... my sister changes her daughter and then packs the diaper bag.

The subject of packt is still meine Schwester, even though it is not repeated.

You could repeat it if you wanted:

..., und meine Schwester packt danach die Wickeltasche.

But that sounds less smooth unless you want extra emphasis.

Because the subject is omitted in the second clause.

After und, the sentence continues with another coordinated clause. Since meine Schwester is not repeated, the verb comes first in that shortened clause:

• ... und packt danach die Wickeltasche.

If you include the subject, then other word orders are possible, for example:

• ... und danach packt meine Schwester die Wickeltasche.
• ... und meine Schwester packt danach die Wickeltasche.

So packt danach is natural here because the second clause is an abbreviated clause with the same subject understood.

Danach means after that or afterwards.

It links the two actions in sequence:

1. she changes her daughter
2. after that, she packs the diaper bag

So danach is an adverb of time showing what happens next.

It is very common in German for describing a sequence of actions.

Die Wickeltasche is a compound noun:

• wickeln / Wickel- = related to changing a baby
• die Tasche = bag

So die Wickeltasche means the diaper bag or changing bag.

The gender comes from the last part of the compound:

• die Tasche is feminine
• therefore die Wickeltasche is also feminine

That is a very important rule for German compound nouns.

German often uses the present tense for:

• habitual actions
• general descriptions
• vivid narration of a routine or sequence

So this sentence can describe something that usually happens before a walk, or simply present the action as a normal sequence.

English often does something similar:

• Before the walk, my sister changes her daughter and then packs the diaper bag.

Even though it is present tense, it does not have to mean right now.

Yes. German word order is flexible, as long as the main rules are respected.

For example, these are also possible:

• Meine Schwester wickelt vor dem Spaziergang ihre Tochter und packt danach die Wickeltasche.
• Vor dem Spaziergang wickelt meine Schwester ihre Tochter, und danach packt sie die Wickeltasche.

These versions all mean basically the same thing, but the emphasis changes slightly.

The original sentence is natural and compact, especially because it avoids repeating the subject.