Notice in many of the examples of "sentimental" they are kind of "nice" (tender ones) tears often brought on by memories of the past. (nostalgic)
Let's say I had a very troubled childhood, my parents were very mean to me, and I hated them for good reaons well into my adulthood. Now they are dead.
Now more time has passed for me and I sometimes take out pictures of them and see them as imperfect people, young at that time, making mistakes like we all do. Every time I do this, tears well up in my eyes. It feels tender and good to let the tears flow, a release, a kind of personal therapy. I wasn't able to forgive them while we were all still alive.
I'm being sentimental. (And actually reconstructing the past into something it wasn't really at the time.)
You go to a movie. There's a lightly touching scene on the screen but no one else in the movie actually cries tears, during it, but you do. You always do. I say you are too sentimental.
If a kid is down on the floor kicking, screaming and crying, he is not being "sentimental" like you and me. His emotions can't be described as "tender", they are exactly the reverse.
The meanings of the two words are different in the extreme.
I hope that helps.