Groupings over non-atomic elements

Question

I use groupings as below:

Join[
  Groupings[IntegerPartitions[3], {A -> {2, Orderless}, B -> {2, Orderless}}], 
  {x}]

Which generates:

{A[2, 1], B[2, 1], A[A[1, 1], 1], A[B[1, 1], 1], B[A[1, 1], 1], B[B[1, 1], 1], 3}

How can A be restricted so A is not applied to arguments that are both atomic? That is. I want the output to be:

{B[2, 1], A[B[1, 1], 1], B[B[1, 1], 1], 3}

Of course, I can remove the results in which A is applied to two atoms (i.e. two positive integers) after generating the list:

{A[2, 1], B[2, 1], A[A[1, 1], 1], A[B[1, 1], 1], B[A[1, 1], 1], B[B[1, 1], 1], 3}

Is it possible to do prevent generating the cases where A applies to two atoms (integers in this case) by adapting the given code:

Join[
  Groupings[IntegerPartitions[3], {A -> {2, Orderless}, B -> {2, Orderless}}], 
  {x}]

For example, by adding a condition

/, ! AtomQ[x] && !AtomQ[y] 

for an application A[x,y]?

Answer 1

Here's a variation of kglr's answer that doesn't modify A or B. First define a helper function h:

h[A[___?AtomQ] | A[_]] := Sequence[]
h[B[_] | B[]] := Sequence[]
h[a_] := a

Then use the helper function in your Groupings call:

Groupings[IntegerPartitions[3], {h @* A -> {2, Orderless}, h @* B -> {2, Orderless}}]

{B[2, 1], A[B[1, 1], 1], B[B[1, 1], 1]}

Answer 2

ClearAll[a, b]
a = A;
b = B;
a[___?AtomQ] := Sequence[]
b[_] := Sequence[]

Groupings[IntegerPartitions[3], {a -> {2, Orderless}, b -> {2, Orderless}}]

{B[2, 1], A[B[1, 1], 1], B[B[1, 1], 1]}