Hang on, that seems a little strange - you have a cassette tool that fits the 11-speed lockring but not the 10-speed when it’s on the trainer…
There shouldn’t be much difference between the shape of the splines (Park Tool say that their older FR5 has the same spline pattern as the FR5.2), but the photo of your mounted cassette makes it look like there’s very little clearance between the axle and lockring. It could be the inner diametre of the cassette tool that’s the problem. In which case you need one that’s as thin as possible.
The bikehand one linked above looks pretty thin, can’t see the inside of the other one. Park claim 12mm clearance for theirs : FR-5.2 Cassette Lockring Tool | Park Tool, so it might be worth measuring the inside of your existing tool to see if that’s the problem.