Rather than letting the bidirectional algorithm of the browser handle the Hebrew text alone, you need to set the directionality of the <div> or <span> element (or whatever HTML element it is) to dir = 'rtl' (right-to-left). This is not an issue for the Hebrew language forum as much as it is for the programmers of the site to be more cognizant of text directionality. I would script some sort of switch in the prompt element that toggles the text direction based on the language so that the same basic template would work for any language. I have seen numerous cases in Hebrew of punctuation or blanks in the wrong place because of this issue. It comes down to the fact that the Hebrew characters themselves default to a rtl direction, so they show up fine, but since the overall element inherits ltr from the document, then neutral characters, such as punctuation, switch back if they are not immediately bounded by rtl characters. Hence the flipping in this and other cases. Hope that helps.
When you use the pronoun suffixes (such as for possession), then you no longer use the definite article. It is already considered definite. That is true across the board for any noun. אני מחפש את המשפחה שלי. אני מחפש את משפחתי.