I am sorry for your loss. (advice from the Ex-cop in me) The police will not release the body until they are satisified they have gained all the evidence they need. The DA's office has an advocate that will help your mom. If your mother is involved in a church, the pastor/minister will have a help list as well. Besides the basics of all the insurances, ensure she reviews the policy for imdemnity - murder has a higher payout (ugly to think, but if it is there she is eligible usually).
The death certificate should be released - but the full details of cause is usually held until the closure of the autopsy. If he had a will, ensure she gets that taken care of, otherwise it can go to probate. Basics: Mortuary, required by all states - body can't be creamated due to the nature of his death, so a site for the burial and the costs (life insurance will cover most if not all) SHOP around have someone not emotionally driven do it - don't let her call, although most of the folks are nice - it is a business and treat it as such. When picking a location, find out the details, are there additional costs (maintenance - sometimes not included in the initial burial costs). look for bank accounts, mortgage(s) paperwork, car loans, loans in general, credit cards, drivers license, professional licenses, etc.. his accounts will need to be frozen, modified to her name, this will require the death certificate.
Remember to have the police increase their visability around the home. Do more drive bys. Because this was highly publicized - the creapers may add the house/phone to their list. SO, beware of that the increase in drive bys by the police/local law enforecement should help detour this.
In the funeral announcement - Do not list the home address.
I think I got about everything. When we lost my uncle to a murder years ago, and my Granny to a drunk driver, that was our top list. I hope it is helpful. Again, my thoughts and prayers are with you. God Bless!