People here seem to be generally in favour of the OP, unlike the top-contributors on stackexchange. I too think that employers "naturally have the advantage of a power imbalance" (by keinos) and in my opinion they often take that advantage.
As OP I would think about two options in that situation - although I'm not sure if I can judge that well, since I don't have a child. In both cases though I would stop faking bugs.
1) Once OP stops pretending to work a full time job the employer might be smart enough to realize that said OP has more capacities and thus might provide him with more work. From my point of view it's not the employees fault that the employer does not know what's going on with the capacities. They don't give you enough work, why should you pretend to work?
2) OP could be pro-active and inform employer of his increasing capacities. Maybe they provide OP with new work.
It might be that the employer requests the automation-tool later on, but maybe it could be that the employer overlooks the free capacity aswell.
As OP I would think about two options in that situation - although I'm not sure if I can judge that well, since I don't have a child. In both cases though I would stop faking bugs. 1) Once OP stops pretending to work a full time job the employer might be smart enough to realize that said OP has more capacities and thus might provide him with more work. From my point of view it's not the employees fault that the employer does not know what's going on with the capacities. They don't give you enough work, why should you pretend to work? 2) OP could be pro-active and inform employer of his increasing capacities. Maybe they provide OP with new work.
It might be that the employer requests the automation-tool later on, but maybe it could be that the employer overlooks the free capacity aswell.