... I am so worried about them!! I think having this sale I can get enough money then I will give it to them all of it. I don't need any money what matters is they have a place to live. -Do you guys think its a good idea?
-Will they accept my money?
I'm not sure what you have to sell at your garage sale, but generally people haggle over prices so much that the seller doesn't really end up with as much as they were expecting at all. I don't want to discourage you, as I think that the garage sale really could generate some extra funds (especially if you are selling bigger items, electronics, or antiques), but just wanted to remind you that you may not get as much as you were expecting for a lot of work. Oh, and if you are selling antiques (or think you might have something antique that you are selling), it would be better to have an antique shop buy them from you (you would make more money).
Also, with the garage sale, you may be able to help them out on one month's rent, but that won't ultimately be a solution for them and, though, it is really angelic of you to want to help them, you can't help them in this way all the time. It will buy them time, though, and that may help them to look for a place to relocate, etc.
I'm not sure that they would accept your money, if it was given in your name. I think that could make them feel very guilty, awkward, obligated, etc. to take money from you. I am pretty broke right now and have needed to borrow money from my parents and I feel all of those things (plus, my Dad holds it over my head and tries to make me owing him money an excuse for him being so nasty to me, but I am sure that your SO and his Dad wouldn't do that). Could it be a possibility to raise the money and then send it as an anonymous donor? I guess they might figure out it's you anyway, but it would be too late for them to protest.
I also wonder that maybe if they were able to relocate somewhere with less rent, etc., if you giving them money might be more acceptable for say moving costs? Oh! Another idea that maybe won't help with rent, but would still allow you to help them is to get some pre-paid grocery gift cards for a grocery chain nearby. I am thinking that if they are short on rent, they probably aren't eating much or well. I think the grocery cards are subtle enough that they would seem more like a gift than out and out charity.