He looks like a sweetie- with a mischievous streak! The first weeks with an adult (even a young one) adoption can be a bit challenging, but as you get used to each other, it usually works out great.
If there are any human dominance issues *at all*, don't play "tug of war" or any other "contest" type game where the dog is actually directly challenging you.
With most dogs (probably 99% of them... my experiences with Bandit and an extremely dominant Akita male were absolute anomalies... valuable experiences, but nothing I'd wish on my worst enemy!) "dominance" mostly means "I haven't seen a human worth following... yet". And if you display your worthiness (being steady, and consistent with both loving attention and discipline as needed) the "dominance issues" often disappear like magic.
Davy... I'm glad I'm not turning you off... I surely don't mean to be critical, but you're definitely getting played a bit! Molly sounds like a pup who is very engaged with her humans... which means that she focuses so much on "fun" that she forgets little issues like going potty! If you leave her in the crate at times (basically, any time she hasn't been out AND "went" within the last 2 hours), and then let her out and *immediately* head outside, you should be able to get her trained.
As smart as she is, she should fairly quickly learn that if she messes in the house, it earns her a trip to the crate for awhile. This shouldn't be in the spirit of punishment; don't yell and scream... just show her the mess, express "disappointment" (voice tone means a lot more than the words) and put her in the crate for a bit. (an hour, maybe, unless it is bedtime). Then let her out, and immediately take her outside to "go".
Housebreaking can be time consuming... we usually accomplish it in few days, but it can be an INTENSE few days... essentially someone keeps an eye on the pup, at least peripherally, at all times when they're running around loose in the house. ANY hint of them beginning to sniff the floor, or squat, has us leap up, grab the pup and head out the door with them. It's like a Chinese fire drill at times, but it works! If I notice "scanning" behavior (the pup sniffing out a potty spot indoors) I make my patented "gong show buzzer" sound in my throat (sort of a mechanical buzzing noise saying "uh-uh" as I grab the pup and head for the door. Then we set them down on the grass, and if using "potty command", give it.
You want to know how smart pups can be? Bandit was scary smart... and, of course, patently insane later on! But as a pup, he was a BRAT. Bullheaded, very dominant and absolutely saw no reason why humans should be Alpha!
One evening, when he was about 10 weeks old, we still had papers down, and he was completely paper trained, and starting to go outside a lot more. He was being a snot at supper, chewing on our feet and being pretty rough about it, even when we scolded him and tried to get him to stop. So I got the leash out, and tied him in the corner of the kitchen, so he could reach his papers, but not our feet.
He promptly gave us a "look", stomped over to the papers and peed. It was NOT a biological need- it was a comment! And then, he looked at us, walked over to a couple of bags of groceries which had been sitting on the floor all afternoon, waiting for me to find time to put them away, gave us that look again, and deliberately set his teeth in a bag, and ripped it open, spilling the contents!
It was pure temper tantrum... once he got it out of his system, he sat down and behaved for the rest of the meal!
THAT was the type of pup I NEVER want to see again!
Molly will be just fine... you're just going to have to put some effort into staying ahead of her! It sounds like she may have a bit of a lazy streak, too, where hey! The floor worked just fine the last time... why not? LOL! But it probably also is that she doesn't quite know HOW to ask to go out! (oh, and every time you take her through that door, you ask 'do you want to go out?" or otherwise use "go out" in a sentence. Dixie "nudges" me when she wants something... pushes my leg or arm with her nose. Then I have to figure out what she wants! I'll ask "do you need to go out" and if that's what she was trying to tell me, she'll trot to the door. If not, she'll stay sitting next to me, clearly wanting attention for a bit.
But it took some time to teach that!
It's funny... writing some of this, I have to really *think* about what we do... it's so automatic after almost 40 years of training pups! I hope I'm explaining it understandably!
Summerthyme