As a Muslim, is it your own responsibility to make arrangements for your grave?
Nope. This is not recorded anywhere Prophet (pbuh) asking us to do this .
Or can and should you leave it to others to sort out after you've passed away?
As you discussed in the rest of your question, you need not bother if you're in a Muslim community, but if you're not, then let's see further. But, to simply answer "Can you do this", since it is a new issue, it depends on the situation which you're involved in. Can't say for sure in general that if it is allowed or not allowed. But, simply continuing with your example...
what if you live in a country with hardly any Muslims, where you have no relatives or family, other than your wife and very very young children
Nice example. But, in general I would like to say, believers are commanded to migrate. More can be read from here.
And I'm not sure, up to what extent the arrangements of grave you're talking about. But, one important thing to consider is this...
Verily, Allah! With Him (Alone) is the knowledge of the Hour, He sends down the rain, and knows that which is in the wombs. No person knows what he will earn tomorrow, and no person knows in what land he will die. Verily, Allah is All-Knower, All-Aware (of things). (Qur'an 31:34)
So, keeping in mind that thing, I can say it is slightly impractical to achieve the thing which you're describing.
Are you supposed to leave the burden of your death and the arrangement of your grave on your wife's shoulder, so she does all the running around to arrange your funeral and the plot of land to bury you in, and look after the very young children at the same time?
Reserving a plot of land is directly linked to this question "Can I reserve my favorite graveyard / burial ground / cemetery for myself?" and it depends on what your intentions are. Here, your intentions are not so as to burden your wife, so I think it is OK, if you reserve a plot. But your intentions should be plain and simple saying "If I die in this place, then so and so is the place I've reserved and you can bury me there". No issues.
May the creator guide us all.