Dear doblet, i am a registered veterinary nurse, with 17 years experience, so hope i can help you a little here. I am also an avid feline fan, and have had many, many cats myself, and especially enjoy aspects of 'feline behaviour'!
I have recently had a baby, and through the health and safety aspects of my work, i was in fact allowed to empty cat litter trays - provided i always wore gloves,and washed my hands thoroughly afterwards - obviously, avoiding the tray when there was any diarrhoea.
Cats absolutely hate change with a passion! They get so very stressed out, and as a result, will 'toilet' in different places to usual.
It is, as you already know, extremely important to always keep the tray as clean as possible, as cats are immaculate creatures, and hate using a soiled tray!
They also don't like using a tray if other cats have been in it - i know it is a pest, but try to have several trays dotted about, ideally one for each cat!
They will not 'toilet' anywhere near their food - so this may be an option for you - to move their food to the areas they are toileting in? - only if always going in the same places though!
Wash the soiled areas thoroughly with biological detergent/washing powder etc. This will kill the 'smell'.
There is no great way to prevent her from soiling in the house, but you need to try and make her as stress-free as possible.
Make sure she has plenty 'high up' places to sleep, as when cats are stressed, they like to be 'high' to see what is going on, in case there is a threat around.
If you see her sniffing around, looking distressed, pawing at the carpet etc...try and catch her and put her in the tray, to encourage her to 'go'. If this works, you could move the tray nearer to the door, and gradually get her to go outside. Have you tried encouraging her to go out and in the catflap?
There are great diffusers/plug ins now available too on the market - you can get from your vets, and am sure also from petshops etc.... Feliway is one, is is great, you can get the spray which can be used directly on areas in the house, or the plug in diffuser, which lasts for a couple of months (but does take a while to work, and needs to be constantly plugged in to work) This releases the natural pheromones that the lactating queen secretes when suckling kittens, which soothes cats, and speaking from personal experience, it DOES work!
Also, there is a capsule of milk protein, called Zylkene, which you can get from your vet nurse. It is not a 'drug' - so nurses can dispense it. It is also fab. Capsule can be broken up and sprinkled into food. Again, it takes a little time to work. Both of these things are really good, and have helped my cat with the stress of a new baby! I have dispensed these 2 items to LOTS of clients at work too!
Hope this helps you a little.
Julie x