Marie - the confusion maybe as a result of your understanding/use of the term trustees.
Private trusts can be created as a result of the wills, agreements etc that you refer to but they may not then lead to a change in the register re the legal ownership.
The trust can be protected in other ways - see our PG 24 with regards how certain restrictions can protect such a trust/arrangement -
Private trusts of land (PG24) - GOV.UK
Transferring the title to the three of you would indeed make them legal owners
The key Q re 'How to proceed?' is one for a legal rep to answer for you. As posted previously we deal with the outcome(s) of what you decide and we have no role to play in answering that Q for you. We simply register what you decide to do, if anything.
Your scenario and uncertainty are not uncommon re such matters. The complexities involved with wills/trusts and then the legal ownership we register create uncertainty hence the need to take professional legal advice to ensure that you all understand the legal position, what options exist and what impact any decisions made then have on you all
IN considering your options it's best to also consider everyone's current personal circumstances re home ownership, health, wills and families and more and what might be 'needed' re the property in the future.
As we deal with the legal ownership we have no role to play in that much wider discussion/understanding