So you are suicidal but in a situation which, were it to continue, you wouldn't ctb in the foreseeable future. The 2 fears that are combining to the decision to ctb tonight are homelessness in and of itself and the loss of capacity to ctb that comes with it, both of which are expected to be realised when you get kicked out, which is likely to be soon. The combination seems overwhelming right now and you have a way out.
In relation to losing capacity to ctb, while you might lose your optimal conditions, the option is not going to disappear. And given your current lack of preparation and the risks it presents to an attempt tonight, I really think those other options are looking almost as good right now anyway.
In relation to becoming homeless, I've been there before for brief periods and it's certainly no picnic. But like so often happens, the fear is worse than the reality. It's not going to be as bad as you expect, at least initially. And in your case there is a chance it won't last - your Mum might be right and your Dad, while he might be genuine now, may shift his stance once the reality sets in.
I'd be tempted in your position to roll with it. See if your Dad follows through and kicks you out, explore the best options available to you in that scenario and just see how you feel with the new reality. The option to ctb isn't going anywhere, even if your ideal method might, and there's every chance your Dad will change his tune when he sees the situation he's put you in, or other relatives step up, or who knows?