I don't recognise the imgur link. Who are they? Chiltern Railways is at https://www.chilternrailways.co.uk/
After putting in the March 16 - that's Saturday so all trains by definition are off-peak on Saturdays - and 2 adults and one child, hit the "Search and Buy" tickets button and scroll way down until you get to Returns. The very first one in your case is Chiltern Railways Family Ticket for £58. You all need to travel together, with the child for this fare, and you're doing that. The £58 gets all of you to Warwick and brings you home, on any train. All the trains taking you to Warwick pass through Banbury so don't worry about that restriction...
The detailed rules are available when you click on the ticket, reproduced below:
Route details Additional information about this fare can be found at
http://www.nationalrail.co.uk/times_fares/ticket_types.aspx
Break of journey: Outward: A break of journey is not allowed.
Break of journey: Return: Break of journey is allowed.
Ticket restrictions available at https://www.nationalrail.co.uk/WZ
Valid only for travel via (changing trains or passing through)
Banbury.
Ticket is refundable
Fare Validity
You can travel from the following stations: London Marylebone, London
Paddington
This ticket is valid from London Marylebone
This ticket is valid to Warwick
Outward - Valid until 16 Mar 2024
Return - Valid until 15 Apr 2024
When can I use an off-peak ticket?
Off-Peak Return tickets are valid for outward travel on the date shown
on the ticket and until 04:29 the following day.Off-Peak Return
tickets are valid for return travel within one calendar month from the
start date shown on the ticket and until 04:29 after last day of
validity.
Off-Peak Day Return tickets are valid for travel on the date shown on
the ticket and until 04:29 the following day. All travel must be
completed by this time.
Off-Peak Day Single tickets are valid for outward travel on the date
shown on the ticket and until 04:29 the following morning.
Off-Peak Single tickets are valid for outward travel on the date shown
on the ticket and until 04:29 the following day.