I don't write letters to people because my handwriting is so bad.
I don't send people hand-written letters because my penmanship is quite poor.
この場合、次のような言い方ができますよ。
ーI don't write letters to people because my handwriting is so bad.
「字が汚いので手紙を書きません」
to write letters「手紙を書く」
my handwriting is so bad「私の字はとても汚い」
ーI don't send people hand-written letters because my penmanship is quite poor.
「私の筆跡はとてもひどいので、手書きの手紙は送りません」
to send people hand-written letters で「手書きの手紙を送る」=「手紙を書く」
my penmanship is quite poor「私の筆跡はかなりひどい」=「字が汚い」
ご参考まで!
I don't normally write handwritten letters because people struggle to read my handwriting.
ご質問ありがとうございます。
この場合、「字が汚いので[手紙](https://eikaiwa.dmm.com/uknow/questions/32680/)は書かない」と言いたいなら、英語で「I don't normally write handwritten letters because people struggle to read my handwriting.」という風に言えます。
ご参考になれば幸いです。