How to group cell type A under cell type B?

This is not a full response, but I have some info that might be helpful.

The subsection issue is caused by the Stylesheet entry for Subsubsection, changing it to the default of 50 should fix it, or anything >40.

Cell[
    StyleData["Subsubsection"], 
    CellGroupingRules -> {"SectionGrouping", 50}
]

The issue is that the default for SectionGrouping is

• Section -> 30
• Subsection -> 40
• Subsubsection -> 50

You are changing Section and Subsection to be 1, but leaving Subsection at its default.

Sorry, I don't have time now to finish looking at the Item/Subitem stuff, but I will mention that you probably want to be working with "GroupTogetherNestedGrouping" rather than "InputGrouping" to stay in the same grouping space as list stuff normally resides (look into the Default stylesheet at "Styles for Body Text > Display > Lists > Bulleted").

SIDE NOTE: Your Stylesheet entries have superfluous CellStyle arguments, the following expression

Cell[StyleData["Subsubsection"], "Subsubsection"]

should simply be

Cell[StyleData["Subsubsection"]]

This is mentioned in the details of the documentation for StyleData:

Style definition cells have the form Cell[StyleData["style"],options].

It doesn't seem to matter, but seemed worth mentioning.

Cheers

Ok so I fixed it:

Cell[StyleData[StyleDefinitions -> "Default.nb"],
 CellMargins->{{21, 3}, {4, 4}}]

Cell[StyleData[All],
 ShowGroupOpener->False,
 FontFamily->"Avenir"]

Cell[StyleData["Title"],
 CellMargins->{{10, 3}, {4, 4}},
 FontColor-> RGBColor[0,0.0,0.6],
 CellGroupingRules->{"SectionGrouping", 9}]

Cell[StyleData["Section"],
 CellFrame->{{.5, 0}, {0, .5}},
 CellFrameMargins->8,
 CellFrameColor->RGBColor[0, 0.4, 0.9, 1],
 CellMargins->{{17, 3}, {Inherited, Inherited}},
 CellGroupingRules->{"SectionGrouping", 10},
 WholeCellGroupOpener->True,
 FontColor->RGBColor[0, 0.4, 0.9, 1]]

Cell[StyleData["Subsection"],
 CellFrame->{{.1, .1}, {.1, .1}},
 Background->GrayLevel[0.95],
 CellFrameMargins->10,
 CellFrameColor->GrayLevel[0.8],
 CellMargins->{{30, Inherited}, {5, 2}},
 CellGroupingRules->{"SectionGrouping", 20},
 WholeCellGroupOpener->True,
 FontColor-> RGBColor[0,0.5,0.8]
]

Cell[StyleData["Subsubsection"],
CellFrame->{{.1, .1}, {.1, 01}},
 Background->RGBColor[0, 0, 0.6, 0.05],
 CellFrameMargins->8,
 CellFrameColor->GrayLevel[0.8],
 CellMargins->{{48, 3}, {0, 0}},
 CellGroupingRules->{"SectionGrouping", 30},
 FontColor->RGBColor[0, 0, 0.6, 1],
 WholeCellGroupOpener->True,
 FontWeight -> "Light"
 ]

Cell[StyleData["ItemNumbered"],
 CellGroupingRules->{"SectionGrouping", 40}]

Cell[StyleData["Input"],
 CellGroupingRules->(CellGroupingRules -> {"SectionGrouping", 60})]

Cell[StyleData["Output"],
 CellGroupingRules->(CellGroupingRules -> {"SectionGrouping", 60})]

Cell[StyleData["Code"],
 CellGroupingRules->(CellGroupingRules -> {"SectionGrouping", 60})]

Cell[StyleData["Program"],
 CellGroupingRules->(CellGroupingRules -> {"SectionGrouping", 60})]

Cell[StyleData["Text"],
 CellGroupingRules->(CellGroupingRules -> {"SectionGrouping", 60})]

Cell[StyleData["Item"],
  CellDingbat->StyleBox["\[FilledSmallSquare]", Alignment -> Baseline, 
   RGBColor[0.0, 0.73, 1]],
 CellGroupingRules->(CellGroupingRules -> {"SectionGrouping", 60})]

Cell[StyleData["SubitemNumbered"],
 CellGroupingRules->{"SectionGrouping", 50}]

Cell[StyleData["Subitem"],
CellDingbat->StyleBox["\[FilledSmallSquare]", Alignment -> Baseline, 
   RGBColor[0.0, 0.2, 1]],
CellGroupingRules->(CellGroupingRules -> {"SectionGrouping", 60})]

But I still can't find a description of what behavior each of the built in cell grouping types provides.