Det er min datter, der husker at give både hamsteren og kaninen vand, selv når jeg glemmer det.

This is a very common Danish structure called a cleft sentence. It is used to highlight one part of the sentence.

• Min datter husker at give ... = My daughter remembers to give ...
• Det er min datter, der husker at give ... = It is my daughter who remembers to give ...

So here, the speaker is emphasizing that my daughter is the one who remembers.

This structure is extremely common in Danish:

• Det er mig, der gør det. = It’s me who does it.
• Det var Peter, der ringede. = It was Peter who called.

So det er ... der ... often corresponds to English it is/was ... who/that ....

In this sentence, der is the normal and natural choice.

Here it introduces the clause that describes min datter:

• Det er min datter, der husker ...
• literally: It is my daughter who remembers ...

In Danish, der is very commonly used when the word being referred to is the subject of the following clause.

Here, min datter is the one performing the action husker, so der fits naturally.

You may also see som in some relative clauses, but in cleft sentences like this, der is especially common and often preferred:

• Det er Anna, der kommer i morgen.

So for a learner, the safest understanding is:

• der here = who/that

Because huske is followed by an infinitive when you remember to do something.

• huske at gøre noget = remember to do something

So:

• hun husker at give vand = she remembers to give water

This is similar to English remember to give, where to give is also an infinitive.

Compare:

• Jeg husker ham. = I remember him.
• Jeg husker at ringe. = I remember to call.

So in your sentence:

• der husker at give både hamsteren og kaninen vand = who remembers to give both the hamster and the rabbit water

Yes, give literally means give, but Danish often uses it the same way English does in sentences like:

• give dyrene vand = give the animals water
• give barnet mad = give the child food

So at give både hamsteren og kaninen vand means:

• to give both the hamster and the rabbit water
• more naturally in English: to make sure both the hamster and the rabbit have water

The structure is:

• give + someone + something
• give hamsteren vand = give the hamster water

Because Danish uses the definite form when referring to specific, known things:

• hamster = a hamster
• hamsteren = the hamster
• kanin = a rabbit
• kaninen = the rabbit

Here, the speaker clearly means particular animals that both speaker and listener can identify, probably the family pets.

So:

• både hamsteren og kaninen = both the hamster and the rabbit

This is completely natural in Danish when talking about known animals, objects, or people.

Både ... og ... means both ... and ....

So:

• både hamsteren og kaninen = both the hamster and the rabbit

This is a fixed pair:

• både kaffe og te = both coffee and tea
• både børn og voksne = both children and adults

In your sentence, it connects the two animals that receive the water.

Because vand here is an uncountable noun, just like water in English.

You normally do not say:

• et vand when you mean water in general

Instead:

• give dyrene vand = give the animals water

Compare:

• jeg drikker vand = I drink water
• vandet = the water when it is specific

So in this sentence, vand means water in a general sense, not a particular identified portion of water.

Selv når means even when.

So:

• selv når jeg glemmer det = even when I forget it = more naturally: even when I forget

This adds contrast:

• the daughter remembers
• even in situations where the speaker forgets

Other examples:

• Han smiler, selv når han er træt. = He smiles even when he is tired.
• Jeg går en tur, selv når det regner. = I go for a walk even when it rains.

Because in Danish subordinate clauses, the word order is normally:

conjunction + subject + sentence adverbials + verb + objects

Here:

• når = conjunction
• jeg = subject
• glemmer = verb
• det = object

So:

• når jeg glemmer det = when I forget it

There is no special inversion after når. Danish inversion usually happens in main clauses when something other than the subject comes first.

Compare:

Main clause:

• I dag glemmer jeg det. = Today I forget it.
  • Here the verb comes before the subject because I dag is placed first.

Subordinate clause:

• når jeg glemmer det = when I forget it
  • No inversion

Here det refers back to the action or responsibility already mentioned: giving the animals water.

So:

• jeg glemmer det literally = I forget it but naturally = I forget to do that / I forget to give them water

Danish often uses det to refer to an idea, action, or whole situation already mentioned.

For example:

• Han sagde, at han ville komme, men han gjorde det ikke. = He said he would come, but he didn’t do it.

In your sentence, det stands for:

• at give både hamsteren og kaninen vand

In everyday speech, some speakers might say something shorter in certain contexts, but in this sentence det is very natural and helps complete the meaning clearly.

• selv når jeg glemmer det = even when I forget it
• without det, selv når jeg glemmer would feel incomplete to many speakers, because glemme usually needs something: what is being forgotten?

So keeping det is the normal and idiomatic choice here.

Because Danish does not usually combine a possessive like min with the suffixed definite ending.

So you say:

• min datter = my daughter not
• min datteren

Similarly:

• min bil = my car
• mit hus = my house
• vores hund = our dog

The definite ending is used without a possessive:

• datteren = the daughter

So:

• min datter = my daughter
• datteren = the daughter

Yes. Danish punctuation regularly uses a comma before subordinate and relative clauses, and many learners notice that Danish commas can appear more often than in modern English.

So in:

• Det er min datter, der husker ...

the comma separates the main part from the following clause.

You will often see this in written Danish:

• Manden, der står derovre, er min lærer.
• Jeg bliver hjemme, når det regner.

Comma rules can vary slightly depending on whether someone uses grammatical comma or new comma, but in learner materials you will very often encounter commas in places like this.

A useful way to understand the sentence is to strip away the cleft structure:

• Min datter husker at give både hamsteren og kaninen vand, selv når jeg glemmer det.

That is the more direct version:

• My daughter remembers to give both the hamster and the rabbit water, even when I forget.

So the original sentence is built from:

1. a basic statement: Min datter husker ...
2. an emphasis pattern: Det er min datter, der ...

This is a very helpful trick when reading Danish: if a sentence starts with Det er X, der ..., try mentally rewriting it as a simpler sentence:

• X + verb ...