I'm not a big fan of T & G since it requires you to mill a tongue and when you do you lose 1/4 to 1/2" of your wood. A spline is basically the same joint except that you groove both sides and create the spline from another board or from plywood. It sounds like these boards will have exposed ends so that the tongues would be visible so that would be a consideration.
However, it also sounds like these boards are going to be exposed to the weather so I don't recommend splines or T&G. The water the boards will absorb will cause major issues with the structure as well as promote rot in the joint itself if water goes into it. In a situation like that most garden gates are built with small gaps (1/4" to 1/2" e.g.) to allow for the expected expansions and contractions the wood will experience and they are held on with mechanical fasteners rather than glue. Mechanical fasteners will allow some movement while every glue joint I've ever tried failed. The frame you attach the boards to are the support frame which hold it all together which is usually the "Z" that is the standard frame.
This is probably not what your wife wants but is the practical solution.
However, it also sounds like these boards are going to be exposed to the weather so I don't recommend splines or T&G. The water the boards will absorb will cause major issues with the structure as well as promote rot in the joint itself if water goes into it. In a situation like that most garden gates are built with small gaps (1/4" to 1/2" e.g.) to allow for the expected expansions and contractions the wood will experience and they are held on with mechanical fasteners rather than glue. Mechanical fasteners will allow some movement while every glue joint I've ever tried failed. The frame you attach the boards to are the support frame which hold it all together which is usually the "Z" that is the standard frame.
This is probably not what your wife wants but is the practical solution.