This speaker is calling his/her own father 母の夫 or 彼女の夫, but it sounds really awkward at least in Japanese. While it's grammatical, the listener will probably think the speaker has some complicated reason not to call his/her own father father.

The first sentence looks perfectly natural and there is almost no ambiguity. If you really care, you can make it more explicit simply by saying 母はいつも、単身赴任中の私の父のことを案じている. As you know, we do not say 私の commonly in Japanese, but it's still much better than saying 母の夫.

This speaker is calling his/her own father 母の夫 or 彼女の夫, but it sounds really awkward at least in Japanese. While it's grammatical, the listener will probably think the speaker has some complicated reason not to call his/her own father father.

The first sentence looks perfectly natural and there is almost no ambiguity. If you really care, you can make it more explicit simply by saying 母はいつも、単身赴任中の私の父のことを案じている. As you know, we do not say 私の commonly in Japanese, but it's still much better than saying 母の夫.

In rare cases where your mother is worried about your grandfather, you can say something like 母はいつも、まだ現役で単身赴任中の祖父のことを案じている.

You are calling your own father 母の夫 or 彼女の夫, but you should not do this. This is really awkward, and the listener will probably think you have some complicated reason not to call your father father.

The first sentence looks perfectly natural and there is almost no ambiguity. If you really care, you can make it more explicit simply by saying 母はいつも、単身赴任中の私の父のことを案じている. As you know, we do not say 私の commonly in Japanese, but it's still much better than saying 母の夫.

This speaker is calling his/her own father 母の夫 or 彼女の夫, but it sounds really awkward at least in Japanese. While it's grammatical, the listener will probably think the speaker has some complicated reason not to call his/her own father father.

The first sentence looks perfectly natural and there is almost no ambiguity. If you really care, you can make it more explicit simply by saying 母はいつも、単身赴任中の私の父のことを案じている. As you know, we do not say 私の commonly in Japanese, but it's still much better than saying 母の夫.