These plays are hard to sort out on-line, without seeing them. Here are some things to consider...
First off, you will have to get rid of the notion of a catcher blocking "part of the plate". If she does not have the ball, she must provide the runner will FULL access to any part of the plate the runner chooses to run to. You can't block off half the plate, or some of the plate, and force the runner to alter her path to the sliver of the dish that you've left open for her. The runner must have access to the ENTIRE plate.
So long as the runner was doing nothing more than running straight to the plate, if the catcher does not have the ball then the runner can go straight in standing up. If the catcher doesn't have the ball and that impedes the runner- to whatever portion of the plate she chooses- this would be obstruction.
If the runner altered her path away from the base, contacting the fielder when she would not have otherwise, then you might have a case for interference.
If the runner crashed into the fielder with malicious intent (umpire judgment) then the runner could be ejected. Generally, running straight to the base in an effort to aquire it is not malicious intent. The runner would need to show some extra action, like throwing a forearm, pushing or swiping at he fielder.
Note that some rules sets have slightly different interpretations on this play. For instance, in high school softball runners are required to avoid, or attempt to avoid, a fielder in the act of receiving a thrown ball. Under ASA rules they are not. Others may have even different requirements.
The "slide or avoid contact" concept in ASA softball applies to a play where the fielder is already in possession of the ball and waiting to make a tag. The "slide or avoid" requirement does not apply when the fielder has not yet gained possession of the ball.
Just because there was contact on the play, it does not necessarily mean it was illegal contact.