No one can guarantee you what will happen in the courtroom, but....if her own parents are willing to come in and testify to her alcoholism, that's pretty powerful evidence. That combined with evidence of three prior DWIs should put you in a pretty good position for getting primary custody, and if you're going to get primary custody, it's pretty likely that the judge will give you exclusive use of the house - to minimize the impact the case has on the kids, if for no other reason.
I agree with Attorney Lafleur but want to expand upon his answer.
If her own mother and father are willing to testify, it's powerful evidence. Your own testimony as to how often she drinks, how much she drinks, what she drinks and the effects it has on her will also be useful. You can also ask for alcohol testing (normally it's a swab) in that temporary orders hearing.
You're also going to want to get certified copies of those DWIs so you can introduce them into court. Even if you testify as to her alcoholism, it's still not going to be a slam dunk until you prove everything up and get it into admissible evidence. If she hires an attorney, you're going to have a tough time on this one even with all this evidence.
I'd strongly recommend consulting a local attorney. However, if you guys can agree on what's going to happen, you might not even need a hearing.
Considering her parents are willing to testify as to her drinking problelm, she has 3 DWIs and has been in rehab 3 times, I think it is likely that the judge will believe she is an alcoholic. It is quite likely that you will be able to stay in the house to minimize disruption for the kids and the kids would stay with you. Her visitation with the children will likely be supervised. Simply being "sober" is not enough for the kids to be placed with her. I have a background in drug and alcohol counseling. It is very common for a person becoming sober to have "slips" every few month. Once she has been sober with no slips for 18 mos to 3 yrs, you might consider allowing the kids to live with mom - or not. There is no reason that the children should not live with the more stable parent.
I recommend that you consult with an attorney regarding this matter.