Yes, female dogs do mark. Four years old, and still submissive peeing, I can understand you deciding "no" -- it would be one thing if she were less than 18 months.
I was lucky. I found a rescue group that happened to have some 6 month old siblings they'd pulled from an out of state kill shelter and one of them happened to be exactly what I was looking for -- I actually think she and I have met before but that's a different story ;-)
I do think you have to be very very clear on exactly what you want. I've thought about this a lot and one of the problems is that most people -- "amateur dog people" you could call us -- have only lived with one or two dogs our entire lives. (E.g., family dog growing up, maybe, then we adopt one when we get settled somewhere as adults -- one dog homes, each dog lives around 15 years . . .)
But dogs are so complex and there's so much variability from dog to dog. It's challenging just to decide "what you want," isn't it? And most of us haven't had all that much practice in "reading dog" -- makes it hard to decide if the dog we're considering is a match.
The dog I had before this one I bought from a "responsible breeder" because I thought that would be a way of working with someone with a lot of experience, and who could guide me to a dog who would be a fit. What a mistake that was. The dog turned out to be extremely reactive, fear aggressive, nippy (and this was congenital -- I do all positive training etc.) I did the best I could for her but she was never an easy dog to live with.
After she died and I was ready to adopt again, I picked one rescue group to work with and was very specific about what I wanted, everything from age to size, and most of all about deal breakers -- resource guarding behavior was one of them (I have a kid); major housetraining issues was another. After having lived with a difficult dog for so many years I knew I needed to be very particular up front.
Another problem that sounds like you ran into is that the rescue people themselves don't always know what they're talking about. So you have to take what they tell you with a grain of salt. It's not malicious, but they're amateurs too, volunteers, and a lot of the information they have is "pass along" stuff. I didn't even get accurate information about my dog's heartworm check status -- you'd think that would be easy, she's either been tested or she hasn't, right?
Throwing out another random thought here, in my case the arrangement was initially a foster situation so that I'd get a chance to live with the dog for as long (or short!) as I wanted before making the commitment to adopt.
As it happens I knew within seconds that she was the dog but I think setting it up as a "trial" at first gave me some emotional space too -- it kept me from pinning my hopes on one particular dog, which kept me clearer. Does that make sense?
I can also relate to having to work with another human on the process too! My ex is also a no-pets person and that added considerably to my stress when I was dealing with the difficult dog. It's bad enough when the dog is driving you crazy :-P
Eh, I'm rambling. I could talk dogs all day. But it sounds like you're in the right place. Be very particular -- that's the best approach. And don't rule out rescues -- people surrender positively gorgeous dogs all the time. I can't believe my little girl was actually on death row at one point -- she is a perfect gem -- I'm sure there's another gem out there waiting for you!