If we have a separate contract on the ownership of the new property would a bank or the courts recognize the contract?

That's a question for a lawyer, not a mortgage guy... In general, there can be agreements outside of mortgage, however if these agreements were made prior to the purchase of the property, then it's illegal if it's not disclosed to the lender, and if you disclose it to the lender, they will not approve your loan. In certain states (like my state of AZ).. Any ownership agreements that have to do with real property, must be recorded with the county and made public. The lenders will often search county records to see if ownership of properties they have an interest in has changed without the loan being paid.. if they see this transfer, it could cause the "Due On Sale" Clause of the mortgage note, and the loan would have to be paid in full... if you want to know what your rights are in your state, you should contact a local real estate attorney and pay them for an hour of their time... I'm a Broker here in Scottsdale AZ and I only lend in Arizona. If you or someone you know is looking for financing options, feel free to contact me or pass along my information. 480-287-5714 WilliamAcres.com

I am not sure why she doesn't want you on the deed, especially if you are giving her $20k to use toward the purchase. Any contract between you would be more like a Will and not a deed. To insure your right to the home, get on the deed!