Answer: Unfortunately, based on your description it does not sound like a lawn grass would grow well for you. Lawn grasses need ample sun, do not compete well with tree roots, do best in an evenly moist yet well drained soil, and do not tolerate heavy traffic when wet. As you suggested, a ground cover might be a solution for you. You might consider lily of the valley or hostas or ferns in the more deeply shaded areas for instance. Another option might be to encourage the moss and work with native plants to create a woodland type of landscape. You could also set aside an area for the kids to play and cover that with a mulch or gravel rather than try to grow grass. And under the pines, a natural mulch of pine needles can be attractive. Another thing to consider is working to improve the drainage so there is no flooding, for that you would need to work with a trained professional such as a landscape architect who can consult on site about the grading and drainage issues. Your local county extension may also have some suggestions. I hope this gives you some ideas.
Q&A Library Searching Tips