In terms of routeing, the journey from Birmingham Group to Stratford U Group is valid via Warwick Group on map BI. Reaching Warwick requires a double-back between group members Warwick and Hatton (and possibly Warwick Parkway). The routeing point group rule means that this double-back is acceptable but that rule applies (according to the public-facing routeing guide) for "interchange purposes only".
RDG have never clarified exactly what "interchange purposes only" means ( and I know that forum members take different views on it's meaning.)
In any case RDG also say that "any ticket indicated for use in conjunction with a particular journey when using the Journey Planner will automatically be valid for the route and service indicated."
Journey planners have no way of enforcing the "interchange purposes only" rule and they will allow you to buy e.g a Birmingham Stations to Stratford-upon-Avon off-peak day return for £8.40 (or if needed an anytime day return at £10.00) for travel via Warwick on the return leg (including an extended break at Warwick.)
See screenshot:-
Since the off-peak and anytime day returns allow break of journey on both legs I think this should be sufficient to cover your intended journey.