If it is a practical question I can suggest a bypass. Yet I don't know how to manipulate such a task, I can suggest, to create the points as suggested, using a field populated with 1's to restrict number of points generated within each polygon. As long as you don't create more than one point a polygon, you can leave the minimal distance untouched.
Second phase is to figure out if the output stand for your rule of minimal distance; that is using the point distance tool, with search radius set to the minimal distnace you wish, i.e. 200 meters. If the output table is empty, thus you have accomplished your task, otherwise - you have a list of the "problematic" points, which can be replaced by another random points creation, for only those polyogns that contain them. e.g. delete the points which are too close together, select empty polyogns and subset into a tmp. layer, generate random points using the tmp. layer etc.
As you can see this is an iterative process, which might function as an algorithm to solve your question; yet coding or modelling it might be problematic, in particular if your polygons are small in dimension, thus many iterations will be required to receive a valid solution. Otherwise, if your polygons are bigger than the 200 meters dimensions it worthwhile to give it a try manually.
I've thought about a better workflow that can be coded (or modelled, thus coding will be better); however can't code it myself. Yet I hope it might help with the process.
The main idea is to generate a random point (or points) within each polygon separately instead of generate all points together. Workflow follows:
- Sort polygon by area; small-to-large
- iterate by row (starting from the smallest polygon)
- create 1 random point in the selected polygon
- create another random point in the second polygon
- use point distance to measure distance between points, within your chosen minimal distance as a search radius
- Check if output table is empty - TRUE: merge points into one layer AND start phase 4 with the next polygon; FALSE: repeat steps 4 - 6 on the second polygon.