[SalesForce] Approval Process Reassign Functionality Not Changing Record Owner

Is there a reason you are using a User as approver? Approver can also be a queue. What about creating a queue, no users, and assigning that as approver?

I think what you want is :

1) Submitter1 edit and submit the record to Approver1

2.1) Approver1 review/edit record and then must Approve --> the record is going to Approver2. Your record will still be in "Pending" for Approver2

2.2) Approver1 reject --> go to final reject actions, unlock records and Submitter1 will have to submit again

3.1) Approver2 approves --> your record is now approved, do whatever you want (field update, email alert)

3.2) Approver2 rejects --> you have 2 options here, go back to step1(=Approver1) OR go to final reject actions. In final reject actions you can unlock your record(+ field updates), so the oirignal submitter can edit and submit again.

Of course in your approval process setting, you must to enable "System Admin AND approver can edit records"

I hope that can help