If you signed some non-competition or non-solicitation agreement which would prevent you from doing this, then they could sue you to enforce that agreement. But if you did not agree contractually to not work for these people, then you can--a former employer has no legal right to stop terminated employees from working for whomever they want in the absence of an agreement.You write that they sent you a document that you had signed: if it did sign it, and if the document states that you can't work for this family (e.g. you can't work for any of the families who use the daycare), then they could stop you from working for them, and sue you (for breach of contract; that is, violating the agreement you signed) if you work for them. It depends on what the document says or prohibits.