This dog sounds like an excellent candidate for tether training. This is where you tether the dog to you so that you know exactly where she is at all times. This way she can't sneak off away from you to do anything in any of the other rooms of the house.
When you take her outside to do her business, keep her out there until she does what she has to do, whether it takes her 10 minutes of three hours. She CANNOT come back into the house until she has peed AND pooped. As soon as she finishes doing both, praise her to the heavens and take her back inside, but until she is reliably trained, keep her tethered to you to avoid accidents.
As far as the amount of poop she does, what type of food are you feeding her? A lesser quality food is not as digestible, and will result in the dog producing much more stool than with a good quality food. Switching to a high quality food like Canidae or Flint River Ranch (just as a suggestion) will lessen the amount of stool considerably because the dog will digest much more of the food. The stool itself will be different, too, it will be smaller and much firmer.
Ghilly
Ginger has the plan perfect as the dog is already 4 months old. There is one other option which is to take the dog out excessively until she gets comfortable going outside. This is what I do when they are very young and they are house broken rather quickly.
When you take them out so much they start gonig outside and then relate going outside to doing their business. Before you know it they are going to the door to let you know it is time to go.
You must also clean the areas where she has been gonig in the house very well so she won't go back to them. If she keeps picking up her scent there she is going to go back.
Good Luck.
As long as she is fit and well and shows no signs of ill health, this must be normal for her. There are no signs of worms in what she does? Even so, has she been wormed?
First thing in the morning dogs usually need to 'go poop'. Go out with her for a short walk. When she does it, praise her and give her a treat IMMEDIATELY. So she will associate the praise with what she has just done.
A little later, take her out again. If she does it again, praise her again, etc.
If you catch her in the act of doing it indoors, say a strict NO! and pick her up and put her outdoors. You must do this INSTANTLY and don't wait for any length of time to do it, otherwise she will get confused. If she's already done it and you missed it, you'll have to let that one go. But the important thing is taking her out regularly enough to give her the chance to poop outdoors, and to give you the chance to re-inforce that 'good' behavior with treats and praise.