Two old lady cats meet, hissing and peeing ensue

My girlfriend's (usually well-behaved) 14-year-old female cat Anton just moved in with me and my 14-year-old female cat Bunch. After 3 weeks, it's pretty clear they aren't inclined to be friends. The biggest problem is that Anton has taken to peeing in various non-litterbox parts of the house. We've seen Bunch guarding the laundry room, where the cat food and litter box reside, so thinking Anton might be too scared to head into Bunch's territory to use the box, I got her a new one. But so far the peeing continues. Is the peeing part of a turf war of some sort? Help before our house smells like crazy cat ladies live here! 

How did you introduce the two of them?  For some cats; especially older ones who are likely to be set in their ways, this is an essential component of settling them in a new home.  It can be a process that requires weeks to months.  That is completely normal.  This article details the advice we usually give for introduction: http://www.thecatsite.com/a/introducing-cats-to-cats.  I would consider separating Anton and Bunch for a few days and then starting again.  Patience really is key for some cats. 

Be sure you clean any spots they mess in with a good enzyme cleaner.  I use Nature's Miracle.  If you don't get the scent out; to her noses's satisfaction, it may draw her back to it.  Enzyme cleaners help break things down that regular cleaners do not.

I think you are right to get her another litter box.  Anton needs a safe place to go and to be comfortable using the box.  Ideally; a home should have one box per cat, plus one.  My 2 are fine with two boxes; but they are litter mates and have always had this arrangement.  

I hope we can help you get this problem sorted soon.  This kind of problem can be very frustrating.  

Welcome to TCS!  

Thank you for the advice! Starting over and following the steps sounds like a good idea, but I'm not sure I'll be able to follow through on that, because I'm actually moving out of the house in a few days and leaving both cats here with my mom. In the event that I'm not able to try the slow introduction again, does anyone have any experience using the Feliway PlugIns in this kind of situation? Is it possible that product would help the two cats feel more at home with each other and thus stop peeing around the house? I'd rather not resort to expensive methods, but the cats really only have to get along for a few months, at which point Anton can move in with my partner, her actual owner (who's in the process of moving across the country too). All this moving is complicated for the humans involved, and for the poor cats I'm sure it's even more confusing! I just need to figure out a way to keep everybody happy, comfortable and pee-free as possible...