A better option than that would be a Brighton to Crewe Off-Peak Day Return, route Southern & WMT only, then a Crewe to Manchester Off-Peak Day Return. Total cost with Railcard is £35.55 + £9.50 = £44.05. Can be cut down to £41.85 if you get a £6.30 TfW only ticket from Crewe to Manchester (the TfW service is your optimal connection in both directions).
The connections across London aren't great if you use the official connection times; combined with the current reduced timetable you'd have just over an hour each way. You could probably do it in half that time in reality, as you'd be using the Victoria line which has a train virtually every 2 mins and takes 6 mins. The walk at either station will probably take you longer! You also have a half hour connection to sample the delights of Crewe, both ways
So overall journey time would be 5.5 hours each way (5 hours if you made an 'unofficial' connection across London). That's not really great for a day trip - plus if you wanted to use the Off-Peak Day Return BTN-CRE, the first train you could use would be the 08:42 off Brighton, so you'd not get to Manchester before 14:13, and your last train back would be the 18:31.
Unfortunately there's not really any 'middle ground' between the cheap £41.85 Southern, WMT & TfW option and the £79.05 Any Permitted Off-Peak Return (it's also not worthwhile getting an earlier train from Brighton as the Anytime Southern & WMT fare is £76.60!). Whilst there are a handful of itineraries where it's cheaper to split tickets, you'd then be tied to stopping at specific stations or taking specific trains.
If you take the Any Permitted Off-Peak Return, there are no time restrictions on the Brighton-London part of the journey, so you're fine to get to London in time for the first Off-Peak departure to Manchester at 10:20 (which gets you in for 12:28). Your last train back then becomes the 20:15 (or the 21:15 if you fancy a rail replacement bus from Three Bridges!). That's still a 4.5 hour (ish) journey time, mind!