What if you use IN operator and split the search term in a words array:
$args = array(
'role' => 'Subscriber',
'meta_query' => array(
array(
'key' => 'membership_class',
'value' => 'Full',
'compare' => '=',
'type' => 'CHAR',
),
array(
'relation' => 'OR',
array(
'key' => 'first_name',
'value' => explode( ' ', $usersearch ),
'compare' => 'IN'
),
array(
'key' => 'last_name',
'value' => explode( ' ', $usersearch ),
'compare' => 'IN'
),
array(
'key' => 'personal_city',
'value' => $usersearch,
'compare' => 'LIKE',
'type' => 'CHAR',
),
array(
'key' => 'personal_province',
'value' => $usersearch,
'compare' => 'LIKE',
'type' => 'CHAR',
),
array(
'key' => 'treatments',
'value' => $usersearch,
'compare' => 'LIKE',
),
),
),
);