The OP is cross and we all say things when we are cross. Her Walmart comment wasn't meant to offend, and she is only venting. It would be different if she said this to the coworker or other colleagues.
If someone went around telling you their way was better constantly, and interfered with things that were not their business, then generally you'd get annoyed. Being arrogant is an unattractive quality and can turn people's backs up. It sounds like this person does not suggest things constructively but force her opinion on everything.
I can relate to the OP as I have a 'friend' who is arrogant, (although she is also self absorbed and entitled too), and believes everything should be done her way. She criticizes me constantly, and makes comments about things. She thinks she is being 'cool' and everyone wants to hear what she says. Sometimes, I am close to screaming at her to shut up because the way she says things offends me and others. But I realize that ignoring her is the best thing to do, and it is good to know how to interact with these kinds of people.
As for not washing hands, I think that is disgusting. I wouldn't appreciate the notes though. If I had concerns I would take them to the coworker rather than making public statements. Signs and notes often don't make someone change their habits. It is a shame if you have to remind someone of that age to follow basic hygiene rules. The notes may be making the person uncomfortable and there may be a reason why they do not wash their hands.
It is obvious that this coworker is abusing her sickness leave- I mean what is the likelihood that she is unwell only on Mondays?! This affects the OP so she should be rightfully annoyed. You may have other obligations after work and finding child care for the children can cost a lot of money. Yes, she should have to cover for her colleague when she is occasionally ill but not regularly on Mondays. If it continues I would go to the boss and say it is really difficult for you because you have children, a husband and a home to get back to as well as other obligations.
OP, hang in there! I can't blame you for being annoyed, but ignoring it is really the best option. If she overrides authority or acts above you, then just be firm and set a boundary.
Meg~ Sent from my iPhone using DISBoards