If you become joint tenants, neither of you will own a specific share of the properties; it will be your 'partnership' that owns the whole of each of them. So, when one of you dies, those properties won't form part of the deceased partner's estate, meaning that they can't be left to anyone (or to any trust) under the terms of their will. Title to each of those properties, in its entirety, simply passes to the surviving partner.
Therefore any provision in the deceased partner's will that sought to gift the property to a trust would be invalid. However the validity of the rest of their will would remain unchanged.
As it's best not to have invalid terms within a will, it would probably be advisable to re-write them but, as I've said above, your existing wills would remain valid (other than for those parts that deal with the properties) if you didn't do so.