My elderly parents drew up a new will, my dad signed it, however, my mother went into rehab for a broken hip about that time and she has not signed it

It is not clear to me whether your parents created one will which they both were supposed to sign or two separate wills - one of each of them.  If it's the first RUN to a local estate planning attorney and get it done right.  If its the second and it was not done by an attorney, again RUN to a local estate planning attorney and get it done right.   Second you may be the named executor in the will, but you have absolutely no power to do anything until such time as the will is probated and you are appointed as executor by a probate court.   Finally, most attorney's who are estate planners can arrange for tghe appropriate people to assemble in hospitals or nursing homes to facilitate the execution of wills appropriately under Texas law.  It requires more than just signing it.