That is a liability question first, and it deserves counsel's review before more charges are made. Review the actual cosigning terms, liability and ownership of funds rather than assuming the spouses’ obligations are identical. Separately, an eligible spouse and unmarried children under 21 may accompany the principal, each through their own process.
Keep household finances readable
In a hypothetical Saint-Bruno-de-Montarville household, one spouse charges business equipment to a joint card while the other pays groceries from it. Untangling that later is slow. Consider a dedicated account for enterprise spending from the outset. On the immigration side, a qualifying E-2 spouse is generally employment-authorized incident to valid status — check the E-2S notation, Form I-94 or other applicable proof — while dependent children hold no work authorization.
Spouse here means a legally married spouse, not automatically an unmarried partner. A pending investor application or the need to keep the business open does not itself permit the spouse to work. Unmarried children under twenty-one may live in the United States and attend school, but their dependent status carries no permission to work. Children may study but not work, including in the family business, and lose E-2 dependant status at 21 or on marriage.