Relationship probably going to end because of dog issues. Advice? Reassurances?

I am having some issues with my girlfriend and her two dogs. While I will try to spare you the personal details, these issues are significantly damaging our relationship. I apologize for the long post, and thank you in advance for those willing to read it and respond. My girlfriend has a 9 year old male Yorkie and a 2 year old male Chihuahua. Both are not house trained at all. While she claims that they are trained to go on training pads, this is not very accurate as they will go to the bathroom on the floor in the less than two minutes it takes to change out the training pad, and they will urinate or defecate consistently in areas of the house other than on the pad. You cannot let them out of your site for a few seconds or they will go to the bathroom somewhere. The one time the Yorkie was at my house and was out of site for not even 20 seconds, he urinated on my floor, and this was within 10 minutes of having urinated outside. However, if both dogs are caged (as they are whenever they come to my house now) they have managed comfortably and consistently to not go to the bathroom in the cage for more than 10 hours. In addition, the Chihuahua has, on multiple occasions, gone onto my girlfriend's bed and urinated directly on her. In fact, back in January, when the last incident of this nature occurred, she, for a short time, seriously considered finding the Chihuahua another home. I have a big problem with the animals not being house trained. I am a pretty clean, organized person and do not agree with them going to the bathroom in the house. No animal that I have ever had has done this unless it was ill. My girlfriend has no intention of trying to train her dogs at all, and her main reason for this is because she is a nurse and is sometimes gone for up to 14 hours at a time. I can understand her not wanting to leave them that long, but she could hire a dog walker. I believe it is really just an excuse because she doesn't really feel like putting in the effort to train them. She has said many times that she just doesn't feel like taking them outside on a leash. Another issue I have is that the dogs are allowed to climb, run, walk, and wrestle wherever they want, including anywhere on the furniture and in the bed. Similarly, they will walk and climb on anyone whenever they feel like it. They will be running around on the top of the couch, and if I am sitting there, they will climb right down on my shoulder and then down the front of me like I am simply another piece of furniture. They constantly need attention and so will climb on you continuously for that as well. The same thing happens in the bed, where they will just walk right on you like its nothing. This is very problematic for sleeping, as when I stay there they wake me up multiple times throughout the night by walking back and forth over me throughout the night as they get up and down from the bed to go to the bathroom on the floor. If they are trying to climb on me and I pet them but hold them back from climbing up on me and toward my face, my girlfriend will get upset about that. The most problematic incident so far happened last week. It was early morning and I was half asleep at my girlfriend's place and turned the other way from her and the Yorkie who was in the bed at the time. At one point, the Yorkie, completely unexpectedly, walked across my head and my face. This startled me, and I suddenly raised my head a little. This, of course, scared the Yorkie who was standing on my head, and he leaped off and down onto the floor. While he was not injured, my girlfriend flipped out, saying "How could I do that to her dog," that "he's only a small dog" and that him walking on me should warrant that kind of reaction. It has led to many problems between us since the incident. Both dogs bark at anything and anyone that moves. The Yorkie will continuously whine if caged and my girlfriend is not in the room right next to him. It is clear that my girlfriend has no rules nor boundaries for her animals and doesn't have really any intention of implementing any. They are her "babies" as she says and "that is just how they are." She likes to use the excuse that they are just little dogs and so it's "normal" for small dogs to go to the bathroom in the house and climb all over everything and everyone. She says they are too old now anyways and that it would be too difficult to try to train them. She also likes to say that they "are not Golden Retrievers" and this is why they aren't as "controlled" or "trained". I have had Golden Retrievers all my life and it has come up previously about how well-behaved they have all been. She also constantly tells me that because I am in veterinary school, I should be more understanding of how her animals behave. She basically says that because I am in vet school that I should be ok with all of these things I have mentioned. She equates me not being ok with them to "I don't love animals". If the relationship were to continue, eventually we would live together. Since my girlfriend has expressed that she really has no intention of training her dogs or implementing rules or boundaries, and I will not be comfortable living with her dogs then, these issues are probably going to cause me to end this relationship. Therefore, I basically want to make sure that I am not crazy and that my concerns are justified. Is there something wrong with a veterinary student or professional having issues with the problems I mentioned above (not being house trained, climbing all over everything and everyone)? Has anyone else encountered these types of problems before where they are affecting relationships and how often does this occur? Are the excuses for their behaviors, such as that they are small dogs, valid? An important point of debate for my girlfriend and I is that she says that in reality, most people with small dogs are totally ok with them not being house trained and going to the bathroom in the house because it is "normal". Is this true in your experience? She also says that most people are totally ok with small dogs climbing all over everything and everyone because they are small dogs and again, it is "normal". Is this true in your experience? I know the answers to most of these questions but I am really looking for others experiences. Also, I know that these issues are not the dogs' fault, but are a result of lack of owner effort. I love this girl very very much, and I feel that if there weren't these issues that our relationship would be significantly improved. While I want more than anything to stay with this girl, I feel that this relationship is going to end in large part because of the issues with the dogs. She doesn't seem to be willing to do anything about the issues. I have tried for about 9 months to be ok with them and while it is tolerable now because we live separately, I will probably not be ok with the issues if we live together. Thank you all so much for reading.

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