Extending cell definition to CellFrameLabels defin

I'm in the process of creating a notebook that contains a style to write documents. I would like Mathematica to behave similar to LaTeX in the sense that when I write a "Definition" cell then it will write "Definition [Chapter#].[Definition#]".

To see what I mean do the following. In an empty notebook create a cell and modify the style to "Chapter". You can do this by selecting the cell and the going to Format->Style->Other, enter "Chapter".

Now go to Format->Edit StyleSheet.... Enter Chapter in the input box. This will generate a cell labeled Chapter. Select that cell, and click on Cell->Show Expression. At this point select all that text that you see there and replace it with the following:

Cell[StyleData["Chapter"],
 CellFrame->{{0, 0}, {0, 0}},
 ShowCellBracket->Automatic,
 CellMargins->{{42, 27}, {10, 30}},
 CounterIncrements->"Chapter",
 CounterAssignments->{{"Section", 0}, {"Definition", 0}},
 FontFamily->"Verdana",
 FontSize->24,
 FontWeight->"Bold",
 CellFrameLabels->{{
    Cell[
     TextData[{
       "Chapter ",
       CounterBox["Chapter"]
       }], "ChapterLabel", CellBaseline -> Baseline], Inherited}, {
   Inherited, Inherited}},
 FontColor->RGBColor[0.641154, 0.223011, 0.0623026]]

This will change the style of how a chapter cell is displayed. I changed the color and font. The most important thing to me is the CellFrameLabels. Noticed that I have made it so that every time you create a chapter cell it will display: Chapter [Chapter Number].

In the picture above I have created several chapter cells and I have added the text: ": Title of Chapter #".

This is simple enough, we can create any cell, apply a definition and take advantange of counters to label the cells.

I have noticed how some books have definitions enclosed in box. So in this case I would like to create a box that contains Definition. Here is my lame attempt with the definition of the cell "Definition".

Cell[StyleData["Definition"],
 CellFrame->{{0, 0}, {0, 2}},
 ShowCellBracket->Automatic,
 CellMargins->{{27, 27}, {0, 8}},
 PageBreakWithin->False,
 CellFrameMargins->16,
 CellFrameColor->RGBColor[0.641154, 0.223011, 0.0623026],
 Background->RGBColor[0.963821, 0.927581, 0.844465],
 FontFamily->"Verdana",
 CounterIncrements->"Definition",
 FontSize->12,
 CellFrameLabels->{{
    Cell[
     TextData[{
       "Definition ",
       CounterBox["Chapter"], ".", 
       CounterBox["Definition"]
       }], "DefinitionLabel", CellBaseline -> Baseline], Inherited}, {
   Inherited, Inherited}},
 ]

Here is how it looks in the notebook:

Here is the question: Is there a way to make the CellFrameLabels part of the cell? I want the label to have the same background and to be inline with the other text. Here is a screen shot of how I want it to look:

I have made the "label" bold font and blue. This is something that the user should not be able to modify.

I don't think that it's possible to do in the way you want. CellLabels can only be text, while both CellDingbat and CellFrameLabels can be arbitrary cell expressions.

Both CellDingbat -> ... and CellFrameLabels -> {{...,None},{None,None}} work if the cell is only a single line long. But do not automatically resize for multiple line cells (at least as far as I could tell). For example:

Cell["Abcdefg", "Text",
 CellFrame->{{0, 1}, {0, 2}},
 CellMargins->{{30, 24}, {6, 6}},
 CellFrameMargins->0,
 CellFrameColor->RGBColor[0, 0, 1],
 CellFrameLabels->{{Cell[" Definition 1.1  ", "Text", 
   CellFrame -> {{2, 0}, {0, 2}}, CellFrameMargins -> 0], None}, {None, None}},
 CellFrameLabelMargins->0,
 Background->RGBColor[0, 1, 1]]

Putting a CellFrameLabel on the top does not have this problem, but I don't know how to align it to the left...

Cell["Abcde", "Text",
 CellFrame->{{1, 1}, {0, 2}},
 CellMargins->{{30, 24}, {6, 6}},
 CellFrameMargins->0,
 CellFrameColor->RGBColor[0, 0, 1],
 CellFrameLabels->{{None, None}, {None, 
    Cell[" Definition 1.1 ", "Text", 
     CellFrame -> {{2, 2}, {0, 2}}, CellFrameMargins -> 0]}},
 CellFrameLabelMargins->0,
 Background->RGBColor[0, 1, 1]]

I think that maybe the best looking solution would be to include the "Definition ch.def:" in the cell contents.

Cell[TextData[{
 Cell["Definition 1.1:   ", Editable->False, Selectable->False, Deletable->False],
 "Abcdefg"}], "Text",
 CellFrame->{{1, 1}, {0, 2}},
 CellMargins->{{30, 24}, {6, 6}},
 CellFrameColor->RGBColor[0, 0, 1],
 Background->RGBColor[0, 1, 1]]

Make it so that it's not deletable by the average user and it is probably almost as good as a cell(frame)label. It can include counters so that it automatically shows the correct numbering. The only problem is that it does not appear automatically, but if you just copy a pre-existing cell, then that's not too much of a problem.

Edit: Adding an input alias that creates the non-deletable counter

First we get the current input aliases,

oldAliases = InputAliases /. Options[EvaluationNotebook[], InputAliases];

then replace any existing alias EscdefEsc with our new one:

newAliases = 
  Append[DeleteCases[oldAliases, "def" -> _], 
   "def" -> Cell[TextData[
     RowBox[StyleBox[#, FontWeight->"Bold", FontColor->Blue]&/@{"Definition ", 
      CounterBox["Chapter"], ".", CounterBox["Definition"], ":   "}]],(*"Text",*)
     Editable -> False, Selectable -> False, Deletable -> False]];  
SetOptions[EvaluationNotebook[], InputAliases -> newAliases]

Since I don't have your style sheet, I need to set a couple of counters:

CellPrint[Cell["Setting the counters", "Text", 
  CounterAssignments -> {{"Chapter", 2}, {"Definition", 3}}]]

Now I can use the alias in an existing cell - it inherits the styling of the parent cell (unless otherwise specified):

Another option is to make a palette to go with your stylesheet. This would be useful since there's only a limited number of MenuCommandKey values that you can use for your new styles (n.b. overwriting the default ones will just confuse people). See this answer for an example of such a palette.