Unless FIL is cognitively incompetent, they should be able to make their own decisions. They have all the information from the ER and GP to go on. This is a complicated situation and your question is not answerable without more detailed/nuanced information and discussion of pros/cons. Being on Coumadin is either a necessity or a huge liability (quite often both) depending on factors we do not know here on Reddit.
Thank you for responding. Right now they are saying he is not going to cardiology and neurology because GP told him he doesn't need it. (again husband and I do NOT trust this GP and believe the ER). Husband had me call the university and make sure the appointments cannot be cancelled unless they call my husband's number. Our question is will he be fine like this until Monday or should husband intervene with the nuclear option and go collect FIL when MIL is out and take him to urgent care?