I don't allow my daughter to watch TV for a long time because her eyesight gets worse.
I limit her to watch TV for a long time because it makes her eyesight worse.
I try not to let my daughter watch too much TV because it's bad for her eyes.
I limit the amount of TV that I let her watch because it makes her eyesight worse.
TOMさんの最初の文でも正しいですし、don't allow の代わりに１のように try not to let my daughter... を使って言うこともできます。
1) I try not to let my daughter watch too much TV because it's bad for her eyes.
「娘の目に悪いので、あまりテレビを見せないようにしている。」
TOMさんの２つ目の文は、I limit her to watch TV の箇所が不自然なので、２のように言うと良いですよ！
2) I limit the amount of TV that I let my daughter watch because it makes her eyesight worse.
「視力が悪くなるので娘のテレビの時間を制限している。」
ご参考になれば幸いです！
モロッコ 
日本 
