Probate will not begin if all assets are in the trust, that's why the trust and pour-over wills are created. Your statement in your will is essentially the same as what we have in ours.

thanks

I am trying to get her name on the deed for the house along with her mothers.
that way no issues or taxes.
(her and her mom live together but she pays for the house)

that is the main thing. I don't want her out on the street if her mom dies.

I'm not a lawyer, but I know you need one.

You said, "my friend is a single parent with just her ex husband, mother and sister.
none of them have a will."

If the woman has been paying for the house does she have good documentation of that fact? If she does not have good documentation and good justification for getting her name on the house deed it could be contested. Someone could claim she put undue pressure on mom to sign half the house over to her. Even if she has good documentation, she has an ex. If she paid part of the mortgage with marital assets he could claim a piece.
Just having her name on the deed doesn't mean she gets complete ownership if mom passes away. There can be language in the deed saying the survivor gets whole ownership. There is a legal term for that. Again, I'm not a lawyer, but I'm pretty sure that language has to be in the deed.
Get a lawyer soon.

The house should be listed as "joint tenants with right of survivorship" which would bypass any probate process.

If the divorce is final, no worries about the ex. If its not, see an attorney.