Lymington would be about 2-3 hours from Bucklers Hard on Saturday pm. Then leaving about 10.00 am on Sunday Studland would be 4-5 hours from Lymington.
It might just be possible for you to make Christchurch on Saturday but any delay in launch would make tidal gate at Hurst tight.
You do know it is Cowes Week in the Solent and I imagine Bucklers Hard and Lymington will be worse than the M25.