This is an admissibility of evidence issue governed by common law precedents. Here is how courts have ruled on this issue:
In civil cases, it appears that if the evidence was obtained by or though means of an illegal trespass, the evidence should be excluded if offered as substantive evidence. Day & Zimmermann, Inc. 483 S.W.2d 541, 546 (Tex. Civ. Ap. - Texarkana 1972, writ ref’d. n.r.e.) The court in Day properly excluded the testimony of awitness who’s testimony was to be based on observation made while he was unlawfully trespassing on the plaintiff’s property. If the excluded evidence was not “impeaching”, then it is proper to deny admission. Barham v. Turner Const. Company of Texas, 803 S.W.2d at 739. If the evidence was obtained after the litigation has begun, the admissibility can be challenged by Tex. R. Civ. P. 215; Schenck v. Ebby Halliday Real Estate, Inc., 803 S.W.2d at 372-373 (noting that the trial court is authorized to exclude evidence as a discovery sanction.). As this area of evidence is applied to family law cases, one could infer that if the parties are separated and the other party, or their agent, trespasses on the other party’s property to gain access, the evidence should be excluded as substantive evidence, but not necessarily as impeachment evidence.
So, if you lie about something under oath, then the video may be used to impeach your testimony.
I did not find any comparable FLA case cites for free on the web; but they may be found with a subscription to Westlaw software which requires a very expensive monthly fee and yearly commitment. FLA law will most likely be the same as the this because the rules of evidence don't change much from state to state.