some cameras that shoot interlaced actually shoot 1 frame per two fields where the motion is the same
in each field. in this case, interpreting as progressive is actually the right answer.
if not, and you still want to deinterlace, a possible stutter could be from interpreting the wrong field order
top vs bottom(upper/lower).
double frame rate is one kind of deinterlacing called (frame doubling) maintaining all quality.
if you do indeed want 25p, you should know that it has its own problems being panning speed limitations, higher shutter speeds(looking like sav‌ing private ryan) and studder, jerkyness from lack of motion information. that is why you want double shutter as frame rate, shoot 50p with 2x shutter at 1/100th so when you deinterlace it becomes 25p at 1/50th. the formula is: fps/2x fps shutter. you can fix this in post with AE’s timewarp shutter only or reelsmart motion blur.
if you accept all this and understand the limitations of deinterlacing, you now must accept the deinterlacing algorithms.
teranax and alchemist OD both give almost no loss in quality. Other cheaper alternatives such as adobe’s built in deinterlacer, virtualdub’s qtgmc, boris, fieldskit, red giant frames, all don’t post compare the frames to determine if artifacts are unwanted so they will all lose some quality.
using optical flow from 50p to 25p might be slightly smoother than a simple deinterlace if your camera’s cmos doesn’t record perfect
fps. i.e. 60fps would be 1/60.000th second.
https://blogs.adobe.com/creativecloud/optical-flow-time-remapping-tips-tricks-for-best-results/