Ourselves vs us?

A shoe suggests, the better choice is

I am simply haunted by the fear of my family not having enough money to support itself.

Here are the issues as I see them

I am simply haunted by the fear of my family not having enough money to support ourselves

should be

I am simply haunted by the fear of us not having enough money to support ourselves

I am simply haunted by the fear of my family not having enough money to support us

Sounds like you are afraid that your uncles are not rich enough to help support you and your wife

I am simply haunted by the fear of my family not having enough money to support themselves

sounds like you can support yourself, but your family in xxx does not have enough money

Both would be grammatical. The choice depends on the first part of the sentence and the overall context. In some cases, themselves would be appropriate.

EDIT:

In the light of the completed sentence and your further explanation, I would say that the sentence is not one that a native speaker would normally produce, either with ourselves or with us. That is because my family is third person singular and both ourselves and us are first person plural. In a conversation, it would be clear by the time that this sentence was uttered that the family was in financial difficulties. The speaker would therefore say something like 'I am simply haunted by the fear that we won’t have enough money to support ourselves.’

If the speaker had not been included among the family members, then 'I am simply haunted by the fear of my family not having enough money to support themselves’ would have been possible.

The safest general rule, is that you use the reflexive (myself, yourself, himself, herself, itself, oneself, ourselves, ourself†, yourselves, themself‡, themselves) when it refers back to a previously stated noun, noun phrase, or pronoun.

Correct:

I got it for myself.

He got it for me.

Incorrect:

*He got it for myself.

*I got it for me.

Dialects differ on sometimes allowing either or both of the forms marked as incorrect here, but none consider the first two examples to be incorrect.

The interesting thing here, is that there is a switch of person, which means we could consider it in either way (and another). "My family" is a third-person singular term that refers to a first person plural concept (because you are part of your family). Hence we can have:

I am simply haunted by the fear of my family not having enough money to support ourselves.

This treats "my family" as a first person plural concept, and hence refers back to it with ourselves.

I am simply haunted by the fear of my family not having enough money to support us.

This treats "my family" as a third-person singular term, an introduces the first person plural object us as what it is (or may not) supporting.

We can also have:

I am simply haunted by the fear of my family not having enough money to support itself.

Which treats "my family" as a third-person singular term, and then refers back to it.

We cannot though have:

*I am simply haunted by the fear of my family not having enough money to support it.

Because if we treat it as third-person singular at the end, then we are clearly referring back, and so must have itself rather than it.

We could also have:

I am simply haunted by the fear of my family not having enough money to support themselves.

Because we can also consider our family in exclusion to ourselves (that is, I can use "my family" to mean both everyone in my family including me, and everyone in my family except me), and this allows us to treat it as third-person plural.

All of these except for the form using itself are switching person and/or plurality from the first-person singular term to another person or plurality on the basis of the reader's understanding of how families contain people. Because itself does not require any such switching, it's the version that would meet the least objections, and probably the best choice to go for.

† Only used with the majestic plural, which you only use if you are a monarch, pope, or in some cases an earl or higher rank or a few other jobs. That it was controversial when a mere Prime Minster used it, should suffice to convey that it is very restricted in use.

‡ Related to the singular use of they/them and hence condemned by those who don't approve of singular uses of they/them.