Maybe you could post a photo of the machine because I don't know what a Standard 1941 is. I've also moved this topic to the repair section of the forum. As for the rocking issue, maybe you should give the person who repaired it a quick call, because what you're describing doesn't sound normal to me at all.

If yours is a 1941 Underwood, you have a carriage-shifter, prewar.  Just how "loosey-goosey" is this movement?  I highly suspect that as this is a charriage-shifter, whoever cleaned it must have had the carriage off, and didn't align the little wheel on the bottom with the shifter bar on the base.  There is a guide on the bottom of the wheel on the carriage, and instead of having the shifter bar between the guide and the wheel, the guide is resting on top of the shifter bar on your typewriter.  You can try pushing the shifter bar in the middle back just enough for the guide to fall down and land the wheel on top of the bar, or you can remove the rear carriage rail and lift up the carriage just slightly and pop the little wheel back down where it belongs.  I think this method should be the easiest.  I've run into this many times for some reason, and it seemed pretty easy to effect a repair.  Then you should have a relatively tight carriage.  By the way, Royals have a slight play unless their guides are set too tight.  Remingtons, with their several different types of carriage mechanisms that have evolved over the years, have always been tight, and when properly adjusted, have no play at all.