To file for divorce in any state you need to meet its residency requirements. These requirements vary by state. Two additional things that you should consider when thinking about relocating are what the divorce laws are where you are compared to the laws of the state that you are moving to, and what is the impact on any children involved. To the first point, you want to make sure that you aren’t filing for divorce in a state where the divorce laws are less favorable to you. To the second point, courts can and do frown on one parent’s leaving the state without the other’s consent. A lawyer can help you figure out which state would be best to file in and how to negotiate and interstate custody issues.
After the elapse of a period of time, nobody much cares if the reason you only had every other weekend was because the other parent truly wouldn’t “let” you have more time. Although that may very well be the case, and although you may have let your spouse control the situation in order to spare the children the trauma of parental conflict, in my experience the courts are more swayed by the pattern of contact rather than by these “excuses.” The wisdom of Solomon does not apply. 
In all of the states we practice in, both equitable distribution states and community property states, the parties are encouraged to actively participate in, and come to agreement on, the fair division of their marital assets and liabilities. But unless you and your spouse are experts in the financial matters pertaining to divorce, this can be a dangerous path to walk.
The answer to this question varies. The “average” divorce can take anywhere from 6 weeks (or less), to a year and a half or more. How long your divorce will take depends on how well you and your spouse can cooperate, and on the complexity of the issues involved. At Tarshish Cody PLC, our attorneys will do their best to zealously represent your interests while still taking care to resolve your manner in an efficient and cost-effective manner.
A Motion is a paper asking the Judge or Referee to decide an issue in a case. In a divorce matter, a Motion for Temporary Relief allows you to ask the court to issue a temporary order for child custody, child support, spousal support, and certain property issues. The Temporary Order allows you to get needed financial support while your case is pending in court. The Temporary order will expire when the final divorce decree is signed by the Judge and "entered" by court administration.