Käännös - Hollanti-Saksa - he le wat ik me afvraag hebben we nu een relatie...

I give you a much better translation
(because
- "Beziehung" means a business relationship and I really do not think you mean to say that
- "vermissen" is something you would rather say of things than of people; "fehlen" is the better word for it
- "schrecklich" usually is used in a negative context; therefore "sehr viel"
- in the context I think you mean to give a tender hug, which is more than just laying your arms around someone; therefore "Kuschel"
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COMPLETE TEXT TRANSLATION:

Hallo Sexy,
Ich kann nicht warten bis du bei mir bist Schätzchen! Aber haben wir jetzt ein Verhältnis oder nicht? Versprichst du mir, daß du auf mich wartest und in Oktober wirklich kommst? Du fehlst mir sehr viel! Ich liebe dich Liebling.
Kuß und Kuschel Ella

I would choose "Beziehung" instead of "Verhältnis"

Verhältnis is a better word, because it means een verhouding in dutch.

My feeling for the meaning of "ein Verhältnis haben" is that it implies a third person somewhere who is being cheated on by the two having the "Verhältnis".

To have a "Beziehung" would be neutral in this regard. I don't agree with jollyo that its meaning is restricted to business relationships.

I don't know about the difference relatie/verhouding in Dutch. Is it similar?

I agree with Bhatarsaigh.
In Dutch, 'relatie' can refer to a business relationship as well as to an emotional relationship. 'Verhouding' can be honest, but is often used for an illegitimate relationship (affair).

... changed it back to "Beziehung" because this is the translation closest to the original text and does not distort the meaning.