I do not agree that after 2S, your P should double. That double seems to show 2 minors. If this hand is weak for your convention to bid 3H directly, maybe I will agree with 2NT, but transfer to 3H after 3NT. However, i do not like the 3NT after 2NT, N can not see 9 tricks if his P has a weak hand, I prefer to 3C and will be satisfied to a part contract.