From what you are saying, I think you may have a more serious behavioural issue...But I will share that with Lady, if I do not let her out as soon as she scratches at the door, she will immediately go to her bed or a rug and pee there. So I know that if she is at the door I had better let her out because she wont hold it for long. That being said, I do leave her in the kitchen by herself during my work day and she has never had an accident in there.
Also, if she is not spayed it could be a more "hormonal" behavioural problem. I dont know about females, but I know prior to having my parents' male cairn terrier neutered, he would mark in the house and hump everything, and was quite moody/aggressive. He was not neutered until nearly 2 years old, and the behaviour change was DRASTIC. He no longer exhibited any of those negative behaviours almost immediately. The newer puppy in your home may be making Mollie territorial and without those sexual reproductive hormones, some issues may go away. And not to criticize but merely to get you thinking, especially for a female dog, there could be many more negative side affects to not spaying versus spaying. I would suggest reading through some of the discussions we have on here regarding that topic. It is indeed controversial with many opinions, but it may be something to reconsider due to these issues. I am by no means an expert - just something for you to consider and perhaps chat with your vet about.
Lady (1 year old tricolour) & Gracie (3 year old blenheim)
"Happiness is a warm puppy" - Charles M. Schulz