What do I need to do to get Mom's mobile home transferred to me since she's passed?

Find the title for it. The Executor has to sign it over and of course you have to check to see if it has loans or liens against it. You may have to pay sales tax. Many times the park is owed back rent, so you have to check with them too. They may have a copy of the title and DMV registration. They may want you to sign a new agreement with the park.

Did your mother have a will? If the property was left to you in the will, then it will be yours. Other people who could potentially have a claim need to sign a standard form letter that essentially says that the relinquish any claim to the property. The property will then go into probate to make sure no claims can be made on the estate. At the end of the probate period, the property will belong to the person named in the will.

If there was no will, it becomes more complicated. You will need to consult with an attorney about what to do. If there was a will with more than one heir to the property, then the other heirs would need to sign quitclaims before the property could go into probate. It isn't too difficult as long as there is a will and the potential heirs are in agreement.

The first two answers are in the right direction. The Original Will is the most important document existing IF there is one. Probate is tough without that. Don't count on sibling's conveyance of your entitlement to the trailer. Money sucks because it comes between families. Check the county court clerks site for recorded deeds, if a QC had been filed you would see it there with a recording date and book/page number.
I've gone through this issue with family and with the atty I worked with. Before you pay any atty, check with the county for low cost legal assistance., they are usually a huge help.
Best wishes to you for a happy outcome. Nice to dream, isn't it?