Legal Question in Real Estate Law in California

To answer the question in the abstract, there is nothing to prevent a co-owner from suing another co-owner for breach of a contract relating to the co-owned property. Co-owners are fiduciaries of one another, at least in certain contexts, and there used to be some restrictions on suits between partners, but that is ancient history.

Whether the contract is enforceable may just depend upon how well drafted it is.

Your question does not mention how the down payment for the property will be divided, which is a matter of some interest to answering attorneys here, although I guess it really doesn't affect the answer.

Three-way joint tenancies are unusual, although perfectly possible.

From a practical standpoint, I have some reservations about the motivation and overall wisdom for such a plan. If the intention is to pass family wealth to the next generation while avoiding probate, there may be better ways to accomplish the result without complexities and worries, or the downstream necessity to sort out your son's interest from your daughter's. Some kind of living trust might save taxes and future hassles.

I would advise consulting an attorney who specializes in family financial planning, trusts and estates, or the like, for better ideas and a full explanation of why your plan may not be the soundest.

I was confused by your question. If the co-tenant is not a party to the contract, the contract is not enforceable against the co-tenant. To be enforceable, it should be in writing, and be signed by the party to be bound.