In fact, e-mails were used extensively by the Justice Department in its antitrust case against Microsoft. Although the Microsoft case was not heard in Family Court, the principles are the same.
Much of the evidence that the Justice Department presented to the Court of Microsoft's anti-competitive activities was based on intra-company e-mails that officials within the company sent to each other. One key point is that the Microsoft emails could be easily shown to be authentic, that is, they were not forged or manufactured specifically in an attempt to minimize Microsoft's liability.
Question: So, email can be used if its authenticity can be established...but that assumes that there is a digital signature. What if there isn't?
Answer: If there were any security measures taken to guarantee the authenticity of the parties transacting then the email will be valid as evidence in court. Please take note that this is important. The last thing that we want is for difficult ex-spouses to start manufacturing email messages to stir up potential lawsuits or to bolster their claims. A case using email evidence might still prevail if the court is willing to subpoena the ISP transaction logs and the RFC data (assuming the message numbers are still intact).
But without the electronic signature, there's no concrete proof that the person who had been sending those messages is the person himself. One possible exception would be if they copied the email to another person (a friend or significant other)- if the copy can be shown to exist it will bolster the claim that the email was in fact sent by the person you say it was.
Under certain circumstances, email can be admitted into evidence, but that does not mean that the email is not impeachable (capable of being thrown out as evidence). Where the e-mail is against the personal or self interest of the party (as in the Microsoft case, for example), it should be admissible since it is difficult to impeach. It's a bit complex, but the legal implication does exist.
On the other hand, if used to establish proof of a meeting of the minds (i.e. a visitation agreement between two parties) this could easily be impeached, as both parties could no doubt come up with a printed e-mail saying this never happened (essentially "manufactured proof"). Nevertheless, a signature (as appearing in hard copies) should prove to be impeachable. So, the bottom line is that an electronic signature that leaves a person using it no excuse should be able to correct this loophole.
One possibility is to get your ex to provide separate corroboration. What this means is to get her to reference the subject of an email of interest in a hard copy format, such as a written (paper) letter or a recording, such as a message on an answering machine. If you can provide the email PLUS a written letter (for example) where she makes a clear reference to the subject under discussion, this may be compelling, as the second piece of evidence (the letter) bolsters the first piece of evidence (the email). If the claim is made that you forged or manufactured the email, you can show the letter or recording that references the email, helping to establish that the email was in fact real.
All in all, copies of email may be more influential when given to a custody evaluator, as evaluators have more relaxed standards as to what constitutes "proof". (Even if an evaluator doesn't consider the email as proof, the tone and content may still influence them or give them some insight into your ex's behavior and personality.) Emails could be used to show your ex's unwillingness to cooperate, her disregard of court orders or personal agreements, her inability to collaborate on behalf or the child, and other relevant issues. They may also be used to indicate her contentiousness and bias against you, or her willful denial or interference of your parenting time.
Bearing that last paragraph in mind, when sending email to your ex, always write as if your email will be read by the judge, the evaluator, and your ex's attorney- because it may very well be. When writing your ex, always be polite, courteous, and stick to the subject at hand. DO NOT make threats, issue ultimatums, throw insults or comment on anything except the topic you are discussing. An offhand comment or insult made in the heat of the moment may come back to haunt you months or even years later.