I hate to say it but it may be a good idea, I studied psychology for a fair amount of time and it can do a lot of good in these situations, If you both had an eruption of that magnitude then to me there is clearly a lot of pent up anger which is very common after the loss of very close family.
From your "outburst" it would seem to me that you got on better with your Father than your Mother, Counciling may be able to help you to get on better and deal with the situation together, If that is not an option due to either parties refusal then it would be good practice to work out a plan from 2 directions.
Firstly getting you and your mum to keep things civil and provide the understanding that you will need to do it alone.
Secondly to work with you both on an individual level and find coping methods with the anger and sadness at the loss, to confront the loss of your father.
I expect that they will try to get you to work through it as a family at first but they will be able to see very quickly whether that will be possible in the short term, they may work with you individually and then bring you together to work together. Different therapists have different methods.
One thing I will say though is to go in with an open mind, its not easy because they often hit some tender nerves but the minute you close off to them is the minute that that you walk into a proverbial brick wall.