Thank you very much. I just want to be sure that I rewrote this sentence correctly. I added a few more things I need to include in an email.

1) improve spoken English skills by interacting successfully with other students effectively.
2) I'm really sorry for emailing you so late but I've been busy at home both with my son and my mother,who has been diagnosed a serious disease.
3) I think it would be nice if we could start the email partnership among your bilingual eleventh class and my current eleventh class.
4) They have their own class email address to which your students can start addressing their emails.
5) What do you think?
By the way, I hope you had a nice Christmas and I look forward to hearing from you soon. Send my best regards to your school principal, Mrs....

1) improve spoken English skills by interacting successfully with other students effectively. <~~I think this would be better by removing either "successfully" or "effectively" -- your choice!

2) I'm really sorry for emailing you so late, but I've been busy at home both with my son and my mother, who have been ill.

3) I think it would be nice if we could start the email partnership between your bilingual eleventh class and my current eleventh class.

4) They have their own class email address to which your students can start addressing their emails.

5) What do you think?
By the way, I hope you had a nice Christmas, and I look forward to hearing from you soon. Please send my best regards to your school principal, Mrs....