Such arguments are made both in support of temporary as well as permanent relief. Such arguments do not always carry the day, but it is often a consideration that influences judges, even if they deny it. If custody is in issue or you really want to keep the house, try to stay put until the temporary relief hearing, which is your first opportunity to legally compel the other party to move out.
For example, if there are two automobiles, each spouse is usually given one of them. This is especially true if the cars are nearly equal in value. If there is only one automobile, the court often awards it to the spouse who has the greater need for transportation. Extra items of personal property may be awarded to the other spouse so that the overall value of each share remains the same. Retirement accounts and whole life insurance policies are property too.
NOTE: There are many ways to divide real estate in a divorce. The court forms for marriage dissolution (divorce) only give you 1 option -- one spouse gets 100% of the house, cabin, or other real estate, and the other spouse gets a lien. But, you can change the court forms. An attorney can explain other options, advise you about the law, and draft terms to meet your situation. If your divorce involves real estate, you should get advice from a lawyer on your legal rights and options.
In conclusion, my advice to fathers is that they should not despair. If the children would be better off in the father’s custody, that is worth fighting for, and is winnable. I have gotten many fathers custody, even in the most dismal of predicaments. For mothers, my advice is to take nothing for granted. Against a determined father, the loss of custody is a very real possibility which you should take very seriously if custody is important to you.
The Minnesota Judicial Branch maintains a helpful section on divorce at its website, including matters of children and property, an overview of the fees involved in the process, paperwork, and what to expect when you go to court. The site also has a guided flowchart to help you determine which forms you'll need. Also, see FindLaw's article on same-sex divorce.
If any issue pertinent to a custody or parenting time determination, including parenting time rights, is unresolved, the matter may be set for mediation of the contested issue prior to, concurrent with, or subsequent to the setting of the matter for hearing. The purpose of the mediation proceeding is to reduce acrimony which may exist between the parties and to develop an agreement that is supportive of the child's best interests. The mediator shall use best efforts to effect a settlement of the custody or parenting time dispute, but shall have no coercive authority.
In reality, every divorce requires both formal legal procedures as well as some kind of settlement negotiations. In Minnesota, even if you prefer to litigate and leave every decision up to the judge, the rules require that before the Court will decide your case, parties must attempt resolution through some form of Alternative Dispute Resolution, of which mediation is still the most common. 
A divorce can get complicated if the parties have property (real estate, automobiles, vacation property, pensions, jewelry, etc.) or minor children. Usually, the divorce can be done more quickly if the spouses agree on how to divide the property and handle custody and parenting time with the children. Many cases start out with a lot of disputes, but then the parties are able to reach an agreement. Parties often reach agreement after using alternative dispute resolution (ADR) services outside of court. NOTE: If you feel threatened by or unsafe with the other party, you may want to get legal advice or help from an advocate before using ADR.