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The trust may sell the property.
However the gain realized will be taxable for the trust.
In CA all property idenitified as community property receives a step-up in cost basis to its date of death fair market value (or the alternate valuation date FMV if elected by the executor on the estate tax return). Accordingly, your taxable gain primarily consists of the post-death appreciation.
Where you place the property (i.e. in A or B trust) depends on the needs of the estate. This question is wholly dependent on what your trying to accomplish as well as the size of the taxable estate. To answer your question, yes you may split the interest in a property between the trusts if that makes sense.
The survivor's trust (i.e. the "A" trust) has no restrictions and the surviving spouse can co as he/she wishes with property held by that part of the trust. Gains incurred on the sale of the property (i.e. post-death appreciation) will be reportable by the surviving spouse as the "A" trust is ignored for tax purposes.
Property held in the "B" trust is subject to the control of the trustee(s). They will decide in their fiduciary capacity whether its in the beneficiaries best interest to sell the property and reinvest it elsewhere. The "B" trust is considered a taxable entity and will be responsible for reporting capital gains on the sale of trust property and paying the appropriate tax. Ordinary income from the "B" trust is typically passed through to the income beneficiary (i.e. the surviving spouse).
Because it is impossible for me to identify and consider ALL the relevant facts, this advice is not intended or written to be used for the purpose of avoiding penalties, and cannot be used for that purpose.