Firstly Eid Mubarak to you brother. Go to mosque, pray sincerely, pray for clarity of thought, pray that may truth prevail and sin stop.
Next, man up you are 21, you have observed something and derived at some conclusions , your conclusion is "you have a situation at home". Am echoing your take, Sense is not in flashing news to your siblings, sense is in a solution. This situation needs a solution. I honestly believe!
There are more aware, very knowledgeable folks in this forum, I suggest you wait for their inputs. **This thread merits attention**.
Lastly, coming to your situation at home -
1. No to hidden camera, tell you thoughts not to even dare think of it ever again.
Its unislamic. Its definitely a sin against your account. There are better ways of proof. The psychological impact of seeing the recording from a *sick idea* is even worser I think!!!
2. Possibly she has married him and you are not aware
How to find out? Firstly behave mature, do not approach it with anger.
Someone with a good rapport with her, should Ask her. The question should be why she is not married again? Whoever has good rapport - you, one of your siblings, or all you kids together ask her or her parents or her siblings. Intention is to not let the news spread outside your house. Are you okay with your mothers second marriage? Incase you are not yet receptive, reflect deeply, it has merit. Casually ask your siblings, and see how they react to your mothers second marriage. I have recently heard about how teenage daughters made a big drama to their widowed mothers arranged marriage to another widower.
If your mothers marriage turns out to be true (I hope),
- its sad you folks are not aware of it, she might have her reasons for not revealing it.
- Please come back and update the topic.
3. Its time to get her married, if she is not married yet (to him, preferably)
There will be complications, but its better for everyone. your mother needs a companion, kids are kids.
4. you could have rephrased your thread title better..Be here in forums, you will learn a lot. Insha Allah
Because its not confirmed, a rephrase is better. I understand the sentiment and concern you have for your mother, I/we here appreciate that!
Let know your thoughts. Hope all this helps. May Almighty guide as to whats good .... Ameen!