Please help - urination behaviour problem due to stress

Hi...I'm sort of looking for a bit of hope because I am starting to despair about the situation with one of my cats. It all started when this very aggressive neighbouring cat cornered my eldest cat (Maisie) in my utility room. She defecated at the time and I chased him off. The next day she urinated on a bathmat and the day after that on my housemates bed. I changed the catflap to a sureflap (chipped one) but they wouldn't use it straight away (as they didn't like the noise) so he could still get in. I took her to the vets and he gave her long-acting antibiotics as, due to the frequency of the urination, etc, we thought it might be stressed induced cystitis. She continues (I think) to pee outside the litter box sometimes in the utility room (it's large volumes of urine that doesn't smell particularly harsh) so I'm now wondering is it my other cat (her daughter Millie) because she is confused by the presence of the litter trays and smell but doesn't want to use the 2 litter trays her mother is using. (I've seen Maisie using them and it's difficult because the peeing outside the tray happens when I am at work and asleep). I have bought another litter tray yesterday and scrubbed the utility room with simple solutions odour stuff. I eventually got them to use the sureflap catflap but neither of them seem to want to go out it now....although they will come in through it if I put them outside. I noticed the male cat had sprayed the outside of it, so I cleaned it with simple solution and sprayed it with feliway. Maisie is now on the equivalent of kitty prozac to try to make her less stressed because of this other cat (who can no longer gain entry). I don't get angry with them, as it isn't their fault all this has happened, but I am so anxious as I am frightened at what I will find when I get home (I share a house and feel terrible about my housemates bed that was peed on). Will my cats ever be outdoor cats again? Will they ever use the catflap to go outside willingly again? People may think I'm silly but I have only closed off access to the bathroom and the bedrooms but not the downstairs of the house as I am worried confining Maisie to the kitchen and utility room (where she may think he can still get in) will stress her further and exacerbate the situation...sorry about the length of this but any suggestions from more experienced cat owners or similar situations that have turned out for the best will be much appreciated... one last note, they have not used litter trays for the past few years (only when I first got them and when I moved house 6 months ago).