OP -- In Missouri, there is no practical difference between joint physical and sole physical. Neither confers more rights to either parent.
In order to relocate in the future, bear in mind that you will need to give notice (60 days) to the other parent via certified, return receipt mail. You will need to include information that is specified by the statute that Mistoffolees posted. This includes a new parenting plan.
The other parent will then have 30 days - after they receive the letter - to file in court to prevent the relocation. If they DO NOT do so, you are free to relocate and file the new proposed plan with the courts. The other party will have waived their right to contest the move. Active permission from the other party OR the courts is not required.
If they DO file to prevent the relocation, you'll have to wait until the court decides whether or not the child can be relocated. When making the decision whether or not the child can relocate, the courts will consider WHY you wish to relocate, whether the move is in the best interests of the child, and what the child's connection to the community is. It will matter whether or not the other parent lives in the child's home community/school district, how involved they are in the day to day care of the child, and whether that parent is a suitable custodian.
Judges in MO vary greatly on how willing they are to allow relocations, and the odds of moving a child out of their community - when the other parent lives in the community - get slimmer as the children get older.