C#6, 321321 303 bytes
using System.Linq;string F(int x,int y)=>S(x,y)??"~<.,,>~~";string S(int x,int y)=>x<0|y<0?null:y<1?x<1?"":null:y<2?x<3?null:C(x):y*3>x?S(x-1,y-2)!=null?S(x-1,y-2)+"<.,.> ":S(x-2,y-2)!=null?S(x-2,y-2)+",<..>, ":null:string.Concat(new int[y].Select((_,k)=>k<1?C(x-y*3+3):C(3)));string C(int x)=>$"<{new string(',',x)}.> ";
Call F(). The other two functions are helpers. repl.it demorepl.it demo
// Coalesce failed combinations with commaleon
string F(int x,int y)=>S(x,y)??"~<.,,>~~";
// Get successful combination or null
string S(int x,int y)=>
x<0|y<0
// Fail: Out of range
?null
:y<1
?x<1
// Successful: All commas and periods accounted for
?""
// Fail: Not enough periods for commas
:null
:y*3>x
// Not all commapillars
?S(x-1,y-2)!=null
// Try koala
?S(x-1,y-2)+"<.,.> "
// Try crab
:S(x-2,y-2)!=null
?S(x-2,y-2)+",<..>, "
// Epic fail
:null
// All commapillars
:string.Concat(new int[y].Select((_,k)=>k<1
// This commapillar takes most of commas
?C(x-y*3+3)
// The rest each takes 3
:C(3)));
// Generate single commapillar
string C(int x)=>$"<{new string(',',x)}.> ";