Probably not. The probation and police have the lawful right to detain individuals while conducting a lawful search. Given the number of personnel, I strongly suspect that they had some other suspicions about the home or about you and/or your wife. If your wife feels she was unlawfully detained she can consult legal counsel to see how much it might cost for her to pursue legal action in an effort to secure a judgement.
A lot depends on why the officers would not let her record. Though, how do you record when you are handcuffed? If they handcuffed both of you in front, then the handcuffing was ineffectual and someone needs to go back to officer safety 101.2. Is it not a violation of her rights to not allow her to record what was going on in her own home?
You could have your probation violated and revoked. Or, you may simply get a warning to be more careful and next time the consequences will be more severe. It's also possible that if your wife gets the gun back in the near term she will be told to store it somewhere you cannot possibly access it.3. What happens if my PO writes me up for violating my probation even though I honesty did not know any of the 3 things were in my home?
Now, while it MAY have been acceptable under the circumstances to handcuff decline you or your wife from recording the officers, it MIGHT have been improper. What the status of the law is in your state, i cannot say. In general, the police have the lawful right to control any such encounter (such as a probation search) and that can include the detention of all parties in the home. I can't say whether that was standard procedure where you are, or if there was something more. The handcuffing seems a little over the top for a routine search, and if it were a proper search your video would be boring because you'd be recording officers standing and staring at you in a room they already searched because they'd search the room where you were detained before they had you sit down, anyway.
If you and your wife feel sufficiently offended, you can consult legal counsel. Understand that rolling the dice will typically cost several thousand dollars for no guarantee of an award. And until we know why the probation and police folks did what they did, the question is up in the air.

