What I don't understand in this sentence Мы с нашими четырьмя детьми are two things:
why the word "children" is in the instrumental case and not in genitve, as it normally is when preceded by a numeral?
why is even the word дети used, and not ребёнок in the genitive singular as would expect after the numeral "four"?
Russian numerals make me crazy! Thank you in advance to anyone who will solve my problem!
Let's start with your second question: There are numbers - два, три, четыре, and there are so called collective words: двое, трое, четверо. The rules you learned (2-4 take Genitive Singular, 5+ take Genitive plural) are for numbers. Collective numeric words are different, they normally take Genitive plural: двое детей, трое детей, шестеро детей. So, that explains the Plural. Please note that collective numeric words decline and usually act like adjectives (though some forms look different, because they've preserved their archaic endings), so the syntax here is different.
Now about the Instrumental case: the preposition c takes Instrumental. Since четверо is technically not a number, but a numeric adjective, the word for children, дети, should agree with the preposition, and the numeric adjective should agree with the noun: c четырьмя детьми.
I hope it wasn't too confusing.
I must say, the example is weird. I guess it is OK to learn grammar but not something a native speaker would really say (at least, that would be a really rare occasion). Look at the end of the post if you want an explanation for your particular expression.
Look. If your number ends in "один", they are used is as follows:
If your number ends in words for 2/3/4 or 5 and bigger:
By Nominative-looking I mean either Nominative or inanimate Accusative for numbers ending in два, три, четыре. Some examples:
Real Nominative:
Accusative:
Now, oblique forms:
Numbers like тысяча, сотня, миллион, миллиард when they are singular act as nouns themselves. The real "thing" becomes its subordinate, not the other way round (eg. Я под тысячей одеял).
With "тысяча" a rare variant form exists (Я под тысячью одеялами).
Now, back to your expression:
Let's imagine you want to say "I see 4 children": - "четыре" belongs to 2-3-4 group - "дети" is animate, so Accusative looks like Genitive rather than Nominative - use plural of the case required here (Accusative that looks the same as Genitive) - "Я вижу четырёх детей"
First of all, you can omit the numeral and write "Мы с нашими детьми". or "Мы с нашими двумя(двоими?),тремя,десятью детьми".
That's what the form "двое", "четверо" exist for.
As usual, you can try formulating the question to determine which case is needed (and singular/plural).
Мы со сколькими нашими детьми? Мы с нашими четырьмя детьми.
What you expected is perfectly correct with и preposition: мы и четыре наших ребенка. However, normally you would use с preposition ("with", not "and") that requires instrumental.
I think that your confusion resides at the cross-section of three phenomena:
The thing is that, when talking about one's (multiple) children one will invariably use a collective numeral by saying У меня четверо детей rather than У меня четыре ребёнка. With Nominative collective numarals, where the collective word itself is Nominative the dependent word must be Genitive plural. And the plural of ребёнок is дети.
So where the Nominative cardinal number четыре ребёнка is distinctly different from the Nominative collective number четверо детей, they become very similar in, say, Dative: четырём детям and четверым детям.
So, to make matters worse, the speaker in your example (the one who said Мы с нашими четырьмя детьми) is likely to have made a mistake. While s/he would almost undoubtedly use Nominative collective numeral when referring to the children (Наши четверо детей - not Наши четыре ребёнка!), s/he neglected the correct declension when using Instrumental and said Мы с нашими четырьмя детьми instead of the correct Мы с нашими четверыми детьми. While четырьмя детьми is the correct Instrumental of четыре ребёнка, what the speaker most likely wanted to inflect here instead was четверо детей.
Finally, I cannot sympathise enough - Russian numerals are a living nightmare.
I find the original wording to be quite natural for commonly spoken Russian language. For example, a complete sentence involving the phrase above could be:
Мы, с нашими четырьмя детьми, еле поместились в такси
If one was to use the wording четверыми детьми, as suggested by Avi Gordon, this would result in
Мы, с нашими четверыми детьми, еле поместились в такси
These two counting words (числительные) are derived, respectively, from:
четыре - четырьмя (тв. падеж); четверо - четверыми (тв. падеж)
The word 'четверо' is used for animate individuals ('нас было четверо'). The word 'четыре' is used for counting inanimate objects ('четыре треугольника') or counting groups of animate/inanimate objects ('четыре дивизии', 'четыре созвездия', 'четыре класса').
Examples:
This write-up on usage of group counting words (собирательных числительных) mentions the use of the word двадцатеро!
In that spirit, let us carry the counting example up to twenty:
Тhe next counting word would be "двадцать один", and thus the pattern breaks down. Taking the last usable word:
The form двадцатерыми детьми sounds unnatural. The form двадцатью детьми, however, sounds fine. Note that the form двадцатью is derived from двадцать, which is in the counting lineage of the word четыре (rather than четверо/двадцатеро).
Based on the above, I would argue in favor of the form с четырьмя детьми.
