Edit: This answer assumes a jurisdiction in the United States of America based on the use of "Interstate" in the original question asked. If the jurisdiction is outside of U.S. territory, it may not be correct.
So this isn't going to advise you to plead and contact a lawyer in your state for specializing in traffic issues. If you take this matter to court, keep in mind it's not "your word against her." You have a witness in the car, who I presume will testify that she does not recall you shifting lanes without signalling (I'm assuming you and her discussed the stupidity of the whole event and she backed up your claim). So it's your claim word and your fiance's word vs. her word... which tilts the case in your favor.
Additionally, the cops admitted her vehicle did not have dash cam so there's no hard evidence they will be providing that can be determined one way or another. It's clear that you flipped off the cops, but unless they charged you with some violation for that action (I don't know what it could be, as assuming this is in the U.S. that action, while being very rude, can easily be defended as protected political speech... hell, there's a several decades old rap song that basically gives the verbal message of the hand gesture ("[Eff] the Police") and the government cannot punish you for it. This is a little off topic, but if you have some charge for flipping them off you might want to get in contact with the ACLU.).
Either way, you do not have to prove your claim is true, just that it's plausible, while the cop has to prove that not only is her story true, but there's no possible way another plausible explanation could exist at all. And while she's allowed to lie to you on the street about the existence (or lack there of) of dash cam footage, she's not allowed to introduce it as surprise evidence the day of the traffic court hearing and you can object on the grounds of not being allowed to examine the evidence. If the footage does not in fact exist at all, there's a good chance the prosecuter will drop the case, meaning you won't even have to make an argument (but you have to show up for it to be dropped.).
At the end of the day, you need to make the call on perusing this in court and if you want to do it with a lawyer or not. Most traffic tickets are largely considered "not worth it" and are paid prior to court date, which basically is pleaing guilty and then serving your sentence, and she's probably banking on the fine not being worth the time off from your work and the attorney fees. Ordinarily I'd say if you think it's worth your time at work and you think your defense is solid, it's not going to cost you much to argue and most judges I've seen in traffic court tend to knock some sentence off if you tell your side of the story, even if you are still guilty, and if it's going to put points on your liscense that's going to be something to definatly try to get knocked out by the judge, but it's not worth the attorney. However, given the nature of the story (charging you for a crime you did not commit as retaliation for political speech) and the fact you are bringing in the person you love to testify on your behalf (opening her up to perjury (way more serious than moving violations) if your not careful at worst, and a guilty verdict at best if you're not careful) a lawyer might be something to consider... and you can always speak with the public defender to see if they'll help out if you can't afford an attorney (Depending on how your state's traffic courts are handled, you may not be entitled but given the fact that this is some possible constitutional violations).
Also, one thing I'm curious about, when the cop who wrote the ticket talked to you... did you two discuss the flipping off of the cop in the unmarked car? If so, who mentioned that part of the incident first, you, him, or the unmarked cop? If you did not, did you hear the unmarked cop tell the marked cop that you flipped her off at any point (If you did not hear it, do not assume she told him. This will be a problem as the implication I of this situation, is that if cop 2 did not speciffically bring it up first during your interaction, it can speak to a problem in the timeline of when he learned about the gesture you threw... and in that case, it might be that she was getting him to write the ticket so she wouldn't have to testify to false information. Your ticketing officer is required to testify against you... but if cop 2 wrote the ticket, then cop 2 did not see the infraction and is giving hearsay testimony, which should be objected too. She saw the crime, don't let her get away with someone else testifying to her story for her.).