Here is a possible way.  It works, but probably can be refined.  It does not
use Selection.

Sub HereKitty()
Dim r As Range
Dim j As Long
Dim k As Long

Set r = ActiveDocument.Range
With r.Find
  .ClearFormatting
  Do While .Execute(Findtext:="The cat", Forward:=True) = True
     j = r.End
     r.Expand unit:=wdSentence
     With r.Find
        If .Execute(Findtext:="the mat", _
           Forward:=True) = True Then
           k = r.Start
           MsgBox ActiveDocument.Range(Start:=j, _
              End:=k).Text
        End If
     End With
     r.Collapse Direction:=wdCollapseEnd
  Loop
End With
End Sub

What it does:

1.  makes a range of the document
2.  looks for "The cat"
3.  makes the variable j = .End of the Found range.  Remember, when Range is
used with Find the range itself changes to the Found parameters.  This is
important.  This makes j = the .End of "The cat"

4.  expands the Found range to to sentence.

eg.  The cat sat on the mat.  The Found makes  r = "The cat" range.  The
Expands makes it "The cat sat on the mat."

5.  does a Find in THAT range for "the mat"
6.  if Found, that makes r now = the range of "the mat".  The variable k = .
Start - ie.  the value at the start of "the mat"
7.  now we have the END of "The cat" (ie. j) , and the START of "the mat" (ie.
k)
8.  Display whatever is between those in messagebox - but you could do
whatever you want with it).
9.  collapse r.  IMPORTANT!  Otherwise it gets stuck in a loop.

Example:

The cat sat on the mat.

The cat purred its way across the mat.

The code will display:

"on the"

"purred its way across "

I used the Expand to the Sentence, as that seems to be what you want.  It
could be adjusted.