Thank you guys for all the comments.
Since on day 2 in Hakone we will be taking the Hakone Round Pass (Gora-Sounzan-Togendai-Hakone-machi-Moto-hakone-Hakone-Yumoto-Gora), we will skip the Romance Car to go back to Shinjuku.
We will take the Odakyu Odawara Rapid Line line to Shinjuku (looks like a local train, taking many stops -- Y800, 83 minutes), the frequency is pretty good.