Good morning - I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with dogs and cats. I've had my fair share of house training and puppy problems in our home too! I know that it can be frustrating, but with persistence and patience you will get it down :)
13 weeks old is still quite young, developmentally speaking. It doesn't surprise me at all if she's not fully house trained yet. If she's having urinary accidents in the house, it's a good idea to take a urine sample to the vet for analysis to see if she's got a bladder infection. A bladder infection can derail even the most strict of house training routines!
Beyond medical problems, you're still dealing with standard puppy whims - she's not quite got the hang of the house training yet - and that's normal at this age.
There are two important parts to house training a dog: the first is the ‘training’ part and the second is complete and absolute supervision.
Let’s start with training - You can, and should, train a dog to pee or poop just like you can train them to sit. Go outside with your dog, (take cookies!) walk around them yard with them and tell them to ‘go potty’ or whatever word you want to use to teach them to go - just like you’d tell them to sit if you wanted them to sit. When they do go to the bathroom, keep using your 'key phrase' (in my example, I'd say 'good potty!) over and over, then as soon as they're finished, give them the cookie. It's important the the reward happen RIGHT AFTER the behavior (in this case the peeing). If you wait until they come inside, then all they learn to do is come back inside, not necessarily to pee or poop. Depending on how fast they pick it up, you can have your dog pottying on command within a few weeks.
The second part of house training is the supervision part. She can't be allowed to be out of your sight where she might have an accident. I know this is really really tough, but it's really important that you catch her before the has the opportunity to make a mistake, then give her the opportunity to do the right thing, followed by LOTS of praise. If she's been punished for peeing or pooping in the house before, often the 'take home' message is 'don't pee in front of the humans, they get angry and yell at you' which results in a dog that then sneaks off to pee where you can't see. It helps to have them drag a leash around the house attached to their collar so that if she starts to go to the bathroom you can calmly pick up the leash and lead her outside. This is less likely to scare them than you reaching for the collar to 'drag' her outside. Always make sure that once you get outside, you're prompting her to go by using your key words and rewarding her as soon as she's done peeing outside. It's OK to put her in her crate for a short period of time if you're having a really hectic time and can't watch her - as long as she relaxes in the crate and just 'hangs out'.
Please let me know what other questions I can handle for you :) We can chat until I've covered them all!