Spatial join (points in polygon) but also including the "observation count" of each point in the join_count field

When performing the join, you should choose the option "Each polygon will be given a summary of the numeric attributes that fall inside it, and a count field showing how many points fall inside it". (Sounds like you're already using this option.)

PLUS, you need to select the "Sum" checkbox in the Join Data dialogue window.

This way, you'll get a field for the count of points, PLUS another field for the sum of any numeric fields's values.

(Your question said that you wanted this sum IN the join field, not as well as the join field. If this really is the case, then you can follow up with a Field Calculator on the join field to equal the value of the sum field.)

If this does not resolve the question satisfactorily, then you'll need to provide more information, including all details of every step you're doing to perform the join.