Once I/we adopt in our home state, is it valid in all states?

Currently yes. Once an adoption is finalized regardless of the state the adoptive parents are viewed with the same legal rights and responsibilities of a biological parent. For example, if a male couple jointly adopts in Washington and travels to Florida for a vacation, Florida would still recognize them both as the child(ren)'s legal parent. If you moved to another state that would not permit you to adopt, but you adopted prior to moving to that state, your adoption would (currently) still be legally recognized.