Trying to make intersecting pipes filleted of fixed thickenss.

I want a small diameter pipe to penetrate a large diameter pipe to form a T shape.  I want the joint filleted (internally) to improve fluid flow in the pipe but I also want a constant material thickness for casting.

I've tried using the fillet tool on solid parts but because of the curved path of the joint the thickness varies.
My next try was to model the internal surface and then thicken the part but I can't join the two pipe surfaces together so I can fillet the joint.

Is there a standard way of doing this sort of thing?  Is there any way of doing this?  My next try will be make the solid parts and then delete the external faces then fillet and thicken but it feels like a botch and I don't like botches.