These kinds of questions really highlight the need for reform in family law, namely that a post-separation parenting course should be a mandatory part of the pre-procedure process, as well as family dispute resolution.
First, I am sorry for your current situation - the breakdown of a marriage is immensely difficult and emotionally draining, particularly when the bonds of trust have been broken.
However, what you've listed as reasons to remove the mother from the children's lives are reflective of your emotional needs, rather than what's best for the children. I would even argue on the above post that you would be at greater risk of being removed from the children's lives than the mother because it seems you don't recognise any value behind the attachment your children have with her, which poses a risk of emotional harm to them.
The children have a legal right under s 60B of the Family Law Act 1975 to know, spend time and communicate with both parents on a regular basis, regardless of the status of relationship between said parents. Contrary to popular belief, parents don't actually have any rights at all over their children. What the means is that the court is not there to act on your opinion, but rather, it is there to uphold your kids' rights, which is to have a relationship with both you and their mother.
The court determines parenting orders based on the children's best interests, which is outlined in s 60CC of the Family Law Act 1975. The primary considerations are the benefit to the children of having a relationship with each of their parents, and the need to protect the children from harm, and there are a series of secondary considerations, such as the capacity of each party to meet the children's emotional needs.
On the information you've provided, none of it has anything to do with the kids, let alone what's in their best interests or whether they're at risk of harm in the mother's care.
To put things into perspective, how is the mother an unfit parent for going out when she doesn't even have the children in her care? I would argue that's the responsible thing to do, because isn't it better that she's not leaving them when they're supposed to be spending time with her? Further, what court will agree that an unfit parent finds an alternative to driving themselves home after a night out drinking at the pub? That would be more responsible than driving herself home drunk, wouldn't it? And finally, what the mother does with her time really has nothing to do with you, and the court would be inclined to question if you demonstrate the same level of hostility toward the mother while in hearing range of the children, thus posing a risk to their emotional well-being.
Additionally, while it's certainly unfortunate that the mother cheated on you and broke your trust by misleading you about contraception and doesn't live in an immaculate house, those issues make her a person of questionable character, but they definitely do not make her an unfit mother.
If you choose not to support your children's relationship with their mother by denigrating her in front of the kids and trying to exile her from their lives, it will backfire on you in court and it will be more likely that you are removed from the picture for failing to recognise and meet your children's needs. Your children don't just have a right to have a relationship with their mother, they have a fundamental, emotional need to do so, just the same as they have that need with you.
What I suggest to you is speaking to Relationships Australia about counselling on how to deal with separation and divorce, as well as your children's needs and organising a family dispute resolution conference to negotiate care arrangements for the kids.
This may not be what you want to hear, but I find many parents enter the family law system with a very misguided notion about the reality of the situation. Parents are parents in equal measure, and I would truly, truly hate to see your kids grow up without you in their lives because you let your marriage breakdown and your difficult relationship with the mother get the better of you.
I hope this is in some way helps.
