Could you please check the following corrections? Thank you, Writeacher

1) He offers her to let her remain in the country house. Correction: he offers to let her remain in the...
2) She invites her to remain...
3) He offers her to return to her parents.
He offers to let her return to her parents.
He proposes that she should return to her parents.

1. Your correction is correct!

2. OK

3. He offers her to return to her parents. No
He offers to let her return to her parents. OK
He proposes that she should return to her parents. No. Delete "should."