think there are two issues here tbh.
The first is whether she's doing the job she's being paid to do, and the second is the issue re internet usage/looking at other jobs.
With regard to whether she's doing the job you are paying her for, if she isn't, then you need to take her to task over this. If washing/tidying etc isn't being done then you need to discuss with her and work out a strategy for these things to be done.
Re her internet use, how many mn'ers log on to here frm work? - a lot. How many people surf the net from their offices - a lot. Ultimately what she is doing is what an awful lot of employees across the country do every day. If she's surfing constantly while she should be with children then I would definitely have words, but surfing while ds is napping is another thing imo, as she is also entitled to a break.
Also re jobs I think looking at jobs is never a bad thing. I could never have seen my life as staying in one job indefinitely - doesn't mean she's unhappy, but maybe something better suited to her might come along and it's as much her perogative to look for other work as it is yours to consider getting rid of her when your circumsstances change.