Delete a relation in frontend form
I believe you're getting that error because you're supplying an array ([]) for the mother field and the only value in that array would be an empty string ("") if they select the There is no mother option. So what Craft is attempting to save as a relation is [""]. Instead of an array of integer ID numbers, it's getting an empty string which isn't a valid value.

Even if you remove the value attribute of the option tag for the There is no mother option, the field will use the inner text of the tag as the value, so this does not solve your problem either.

One suggestion would be to use radio buttons instead and do the following:

&lt;label&gt;&lt;input type="radio" name="" value=""&gt; There is no mother&lt;/label&gt;
{% for mother in mothers %}
    &lt;label&gt;&lt;input type="radio" name="fields[mother][]" value="{{ mother.id }}"&gt; {{ mother.name }}&lt;/label&gt;
{% endfor %}
{% for user in users %}
    &lt;label&gt;&lt;input type="radio" name="fields[mother][]" value="{{ user.id }}"&gt; {{ user.name }}&lt;/label&gt;
{% endfor %}


This will keep the field empty if someone selects the There is no mother option.