What do you mean by 'limited success'? What is the issue?
PS There does not seem to be anything obviously wrong with your formula, although the syntax could be shortened. Also, there seems to be no result in case both Client and Month are false, which could be throwing PowerApps.
If Gallery2 relies on having grouped_column1 as the Item, then it will fail to populate data if grouped_column1 does not exist.
As an alternative, I would recommend using AddColumns to add a new temporary column that pulls in data from the column you want for GroupBy based on your conditions. Then use GroupBy on that temporary column:
'Renewable Book Test',
"tempcolumn",[put your conditions here]
You can set the child Gallery to
and it would be consistent no matter the condition.