What regulation covers Catagory 1 and 2 assignment restrictions? How long do they last? How can I remove one?

If you mean category 1 and 2 disqualifiers, they are from charges or convictions from earlier in your life. One of the categories is waiverable, the other is not. They can't be removed. If the broadening assignment isn't willing to waiver it, then that's all there is to it. There are however, challenging positions you can accept within your career map that don't require you to be in a position of trust.

Broadening assignments are usually closed until you have completed your KD time, plus there's a lot to go into assignments. KD time, SQIs, just plain timing, etc. If you are that serious about getting off the line for a bit while staying 11B, drop a packet for something like the Army Attache program, SFAB, Recruiting, Drill, Old Guard, etc... Those programs aren't managed by your branch manager, and you don't wait for them, you do it all and get yourself the assignment you want.
You're in the largest MOS in the Army, branch has a lot to worry about, be a lot easier to drop a packet.

You will want to look at AR 614-200. Chapter 8 will talk about the Type I and II disqualifiers, timelines as well as the appeal authorities.