What can I do about Muddy Patches?

Have you thought about regrading your yard or at least parts of it? If that is not possible, how about laying down some landscape fabric and placing gravel or pavers on top? Turn those areas into features of some sort. Plants, fairy garden, etc.

Add additional dirt to the areas when it is dry to level them off and get rid of the low spots. Your grass should cover the new dirt fairly quickly, but if not, sprinkle with grass seed to help it blend it more quickly.

Call your local Cooperative Extension office, tell them the problem & see what they suggest. They should have some solutions for you that you may be able to do more affordably than contacting Home Depot, Lowes or a garden center. My local C.E. agents have always come through for me! Love 'em!!

IMPROVE THE DRAINAGE BY ADDING SAN or make a pond

Make it into a garden area, raise the level a little and use stones or ties to hold the soil, that way you won't drown whatever you plant, Use pavers or something to create pathways between.