I don't see any issue from the perspective of the full time employer, as long as the OP makes themselves available when called I can't imagine why they would care it the OP is working, or sitting at home, nor do I see any reason why they would need to know, provided OP gives them a way to contact him.
For the Part tim eemployer, I would understand a complaint about the OP coming and going at will, however there are pleanty of part time jobs where this is allowable.

