Last fall I added 2-3 inches of compost to my flower bed. Now when I dig in some places the soil is rock hard, and in some places it is soft on top and like muck underneath. If I add more peat moss will that solve the problem, or could I try to use a garden fork and areate it. I am not able to do alot of digging.

Could you hire a student to mix the soil together?

The mucky parts are probably just places where the compost hasn't thoroughly rotted, especially if there is a lot of grass clippings in it. Leave it be and it'll finish the process on its own... As long as you have lots of earthworms about, they will eventually take care of mixing the compost into the hard soil, so, first try digging a spade full of soil and check for earthworms. If there is a good number, you should be OK if you keep the soil/compost topping evenly moist to make it easier for the worms to move about (but don't drown them!) and speed up the composing of any uncomposted material. Mixing the compost in into the soil is always better but, if it's not possible, your friendly, neighborhood earthworms will do it for you eventually! (After all, that's what happens to incorporate fallen leaves into the garden - first they rot and then the earthworms move the leave mould into the soil...) And both the worms and your plants will be happier for the presence of the compost...