Sorry to read your sad news John. Once the death certificate is issued you do what Neil B says, use the Tell Us Once service. Leave all paperwork and accounts untouched and hand over to her solicitor. It is the responsibility of the executors to do all the arrangements.
Rufus is best off where he is and you and Taxi can move to Nyx 2, cats are fine with boats.
There is no hurry to do any deciding. Take your time my friend. You are stronger than you think.