There is nothing in the WA Residential Landlord Tenant Statute that specifically addresses that concern.
http://app.leg.wa.gov/RCW/default.aspx?cite=59.18
So, in the abstract, there is nothing prohibiting the landlord from denying an additional occupant.
Though I can't imagine any landlord objecting unless your daughter has abominable credit or a criminal record.
It's going to come down to what her new spouse's lease says about tenant occupancy. She should read it. And he should be up front with the LL about her moving in, in case time is needed for other decisions to be made.

