I think that could work -- if you mean "take" in the sense of "presume, assume".

Report it as an additional option.

i think you're on to something there bc we say that in english when we assume things in conversation. like:

dude: (standing in a grocery isle looking confusedly at all the diaper options) ...uhhhh.... (scratching head)

dude 2: (noticing dude 1) i take it you're new to this? i was in your shoes when i had my first child. try these ones- they're meant for newborns. (points out some diaper brand)

dude 1: yes. and thanks. (smiles)

Annehmen is a different verb unlike nehmen, which is "take" in English, so consider there is a "an" before nehmen, which alters the verb as "assume" in German.

Because it can't mean that here.

annehmen can be used for accepting, say, a parcel, but not for accepting an opinion or a fact (I would use the loanword akzeptieren for that).

In this context, annehmen can only mean to assume.

In English, the word "that" has (at least) two totally different meanings. If you think about it, you can tell that it serves a different function in sentences like "Can you give me that?" and "I see that you have a bucket". In the first kind of situation we use das. In the second kind of situation we use dass with a comma before it.

The simplified answer: because dass sie Kinder haben is too long to be squished into the middle as Wir nehmen dass sie Kinder haben an, and that would sound confusing even to Germans.

The technical answer: an doesn't actually go to the end of the sentence; it belongs in the "right bracket" position (rechte Klammer) which comes after the "mid-field" position (Mittelfeld) which contains the largest part of most sentences but before the optional "final field" (Nachfeld).

The Nachfeld is very often empty and so the right bracket position is often also the end of the sentence, but dass clauses that are the subject or the object of a verb pretty much have to go there, rather than in the middle -- and then things that go "at the end" (really: in the right bracket) such as separable prefixes or participles end up in front of that clause.

See also https://de.wikipedia.org/wiki/Feldermodell_des_deutschen_Satzes for more than you ever wanted to know about the field model of German sentences.

I agree that the sentence without "that" should be accepted - report it if you'd like.

Correct. The separable verb annehmen means "to assume" (in this sentence).

kinder and kindern are not even German words.

Kinder (capitalised -- it's a noun!) is the plural of Kind, i.e. "children"

Kindern is the dative case form of the plural -- in all other cases, the word is Kinder.

Here, you need the accusative case, as it's the direct object of the verb haben.