My mom mortgaged me when I bought my current house. I'm in BC, Canada so you'll want to check on your local rules. Here, the process of buying a house is separate from the process of getting a mortgage so if you don't need a bank mortgage no one is going to scrutinize where the funds are coming from.
I got a realtor and went through the standard home buying process. As far as the seller and realtor were concerned, it was a cash sale and they didn't care where the money was actually coming from, just that financing didn't have to be a condition. They guided me through the offer process, told me when to get a lawyer to do the purchase paperwork, and the lawyer gave me details on how Mom should make the deposit and final payment. She could also have transferred the money to me and I could have done the payments myself but that was logistically difficult in this case since my credit union doesn't have a branch where I live.
Mom and I then contacted a notary to draw up a mortgage contract. In our case, she's not charging interest since she'd have to pay capital gains tax on any income over the principle. On paper, I own the house. Mom is listed as a lender on the title, exactly the same way a bank would be. If I default on my mortgage, she has the right to foreclose and force a sale. Once the house is paid off, the loan goes off the title. We have a handshake agreement that if my parents die before it's paid off, the remainder will come off my portion of inheritance to keep things fair for my sister.
We could have set up the mortgage agreement first, but it made more sense for us to wait until we had the final numbers from the house sale.
Thanks for sharing your experience! I didn't even think about a mortgage being possible with someone instead of a bank. I'll have to look into if that's possible in Texas.