Well, if its right of survivorship it would automatically pass to the other owners if one of you dies, therefore its a little easier and a bit more protected as it would not have to go through probate. Also, Medicaid will not attempt to take the house if there are other owners living in the house and one of them has to go into a nursing home. Yours is a bit of an unusual situation and I am not sure if Medicaid would really try to interfere with the house under those circumstances.
Also, unless you all put a large down payment on the house there may not be much of anything for Medicaid to go after. They can only go after the share of the equity that the one person would have.
So, if you bought a house for 500k and put 50k down after closing costs etc. you might have 30k in equity. That is only 7500.00 each. If mom has to go into a nursing home I suspect that between you, your husband and your dad, you could figure out how to pay out mom's share of the equity and make Medicaid happy, assuming that they would even go after that small of an amount of equity.