Like this:
{% if age > 18 %}
{% with patient as p %}
<my html here>
{% endwith %}
{% else %}
{% with patient.parent as p %}
<my html here>
{% endwith %}
{% endif %}
If the html is too big and you don't want to repeat it, then the logic would better be placed in the view. You set this variable and pass it to the template's context:
p = (age > 18 && patient) or patient.parent
and then just use {{ p }} in the template.