W..
Typically, if you are offerred a comparable position during a merger (similiar location / similar pay / similar benefits) and you "don't accept" it's the same thing as you "resigning" so you woudn't be eligible for unemployment.
If you want to go PT..... talk to them now and see if they can solidify a deal for you BEFORE the merger so that the new mgmt would HAVE to accept it or lay you off..... THEN you could collect unemployment.
That's if you are wanting to stay with the same company and work PT.
If you are wanting to quit, work PT somewhere else so you can be at home with your kids and just collect unemployment because it happens to fall timing-wise at the same time as the merger.... then that is abusing the unemployment system to your advantage for personal choice.... which, I think, technically is fraud. So, then you would want to be VERY careful about what you say to mgmt or even co-workers about your desires after the merger.
Good Luck.