Both Lovonox and Coumidin are blood thinners, with Lovonox used short term and Coumidin long term. They inhibit the formation of blood clots. My father was on Coumidin for 25 years and had no side effects such as you describe. Without knowing any more details about your situation, the meds may have been prescribed as a precautionary measure. Did you contact his doctor(s) before stopping the meds and what was he being treated for during the 2 hospital stays?
As GranRon says these drugs are blood thinners - they are given to reduce the clotting properties of the blood in case the irregular heartbeats interfere with the way the heart 'fills and empties' with blood as it beats and pauses and residual blood clots form, or by being 'bumpy' it dislodges an existing undetected clot in an artery and blocks an artery somewhere resulting in a stroke or heart attack.
My wife has atrial fibrillation and takses coumadin and has for about two years. Side affects (in her case) is a bit of confusion now and then, and a general slowing down of her brain function. Not much, just enough for family to notice, It has also made her a bit more irritable in general but that might be my fault. I myself have had irregular heartbeat attacks called SVT's where my heart races up to 230 bpm for anything from minutes to a couple of hours and I now take Atenelol daily to slow and regulate my heartbeat. Mine is connected with stomach and digestive problems, and I also have back trouble. For years we both resisted taking medication because I am very drug sensitive and get side affects, and my wife in particular believes in natural therapies more than drugs but got the fibrillation (maybe) because she ignored warning signs (palpitations and high blood pressure) Now she has to take the medication forever or risk stroke or maybe death.
I'm not a doctor but have had these problems for almost 20 years and have been investigated and have studied all of this in great depth. The only thing I have learned for certain is that the medicos do not really know the cause of things, only how to treat the symptoms. I strongly advise you not to stop his coumadin without medical advice first. Maybe the dose is too high? Blood tests called INR will show the level of his anti clotting medication. The risk is not worth it - work with the doctors before stopping the medication because something is wrong.
Also remember that fear and worry often causes us to be angry and argumentive.
good luck