That first suggestion sounds really interesting; adds a bit more of an actual reason to fear being close to her plants instead of just "they do reasonable base damage". The second seems like it would be a bit too powerful however; it means an effective QWE could have you hit by the snare, then hit by a second plant snare right after for a ~2-2.5 second snare (plant attacks once on spawn, pre E, you autoattack them so the plant targets them and attacks the snared person for a double snare).
For the first suggestion, however, it would seem much better for her Vine Lashers to have some interaction with Q in addition to the Thorn Spitters interacting with E, as with the Rylai's change (which even before the change Rylai's made her Q plants 100% better) the only thing Vine Lashers have is lower range and a slow before you finish the Rylai's. Not sure exactly what, but it could be a variation on zone control. Maybe have a Q'd Vine Lasher have a more powerful slow (50%? 60%? But this would buff support Zyra quite a lot and make her even worse to fight as a melee), or do more damage, or try to prioritize champions instead of minions/monsters.