Min søster havde både regnslag og myggespray med, så soveposerne blev ikke våde, og vi kunne sidde ude længere.

At have noget med means to have something with you or to bring something along.

In Danish, short words like med can behave a bit like particles. In a normal main clause, the object often sits between the verb and the particle:

• Hun havde regnslag med.
• Vi tog kaffe med.

So havde både regnslag og myggespray med means that she had those things along with her.

Både ... og means both ... and.

So:

• både regnslag og myggespray = both a rain cover/poncho and mosquito spray

It is the standard Danish way to link two things when you want to emphasize that both were included.

This is something English speakers often notice.

• myggespray is easy to explain: it can be treated like an uncountable substance noun, much like mosquito spray in English.
• regnslag is a countable noun, but Danish sometimes allows a bare singular noun after verbs like have when the focus is on the item as practical equipment rather than on one specific individual object.

So have regnslag med sounds natural and idiomatic.

You could also hear et regnslag, which would sound a bit more concrete: a rain poncho/rain cape.

Soveposerne is the definite plural form: the sleeping bags.

• sovepose = sleeping bag
• soveposer = sleeping bags
• soveposerne = the sleeping bags

The definite ending -ne shows that these are specific sleeping bags already known in the situation, not just sleeping bags in general.

Blive often means become or get.

So:

• blev våde = became wet / got wet
• blev ikke våde = did not get wet

This is a very common Danish pattern:

• blive træt = get tired
• blive sur = get annoyed
• blive våd = get wet

So Danish uses blive + adjective where English often uses get + adjective.

Because it agrees with a plural noun.

The subject is soveposerne = the sleeping bags, which is plural, so the adjective must also be plural:

• en sovepose blev våd = one sleeping bag got wet
• soveposerne blev våde = the sleeping bags got wet

The -e ending is the plural form here.

Because this is a main clause, and in Danish main clauses the negation ikke normally comes after the finite verb.

So:

• Soveposerne blev ikke våde.

That is the normal word order.

In a subordinate clause, the position would be different:

• ... fordi soveposerne ikke blev våde
  = ... because the sleeping bags did not get wet

So English speakers often need to learn that Danish places ikke differently depending on clause type.

Here så means so / therefore, and it is functioning as a coordinating conjunction joining two main clauses:

• Min søster havde ... med, så soveposerne blev ikke våde

After this kind of så, Danish keeps normal main-clause order:

• så + subject + verb

So så soveposerne blev ikke våde is correct.

Compare that with så used as an adverb at the beginning of a clause:

• Så blev soveposerne ikke våde.

There, inversion happens because så is taking the first position inside the clause.

Here ude means outside / outdoors.

In Danish, sidde ude is a very natural way to say sit outside.

• Vi kunne sidde ude længere = We could sit outside longer

Udenfor is also possible, but ude often sounds simpler and more idiomatic when talking about being outdoors in general.

A rough distinction is:

• ude = out / outside / outdoors
• udenfor = outside, often with a stronger sense of location relative to something

So sidde ude is the expression many Danes would naturally use.

Længere is the comparative form of lang in this time-related use, so it means longer.

• længe = for a long time
• længere = for a longer time

So:

• vi kunne sidde ude længere = we could sit outside longer

The comparison does not have to be stated explicitly. It usually means longer than otherwise, longer than before, or longer than we would have been able to without the spray/rain protection.

Because the sentence is describing a past situation.

• havde = had
• blev = became / got
• kunne = could

So the whole sentence is anchored in the past:

1. the sister had those things with her,
2. as a result the sleeping bags did not get wet,
3. and they were able to sit outside longer.

This is a very normal narrative sequence in Danish.