You would need to sue your half-sister in small claims
court for the amount that you are owed for the security deposits that you gave your sister cash for, as well as for the child care money that you had agreed upon.
I have to be honest with you and inform you that proving verbal contracts is not an easy thing, since they normally wind up being he said/she said types of situations. So you will need any type of record you can get to support your claim. For the child care amount, hopefully you have the specific dates where you provided childcare and some notations about when this occurred.
For the security deposit, if you can get some records for the cash (bank account records are best but any other types of records you can use would help) to demonstrate that you and/or your brother had received that amount in cash around the time that you paid the security deposits would be helpful.
You will need to go through your half-sister to get this money, since the apartment complex held up its contractual obligations by refunding the security deposit to the person who paid it to them.
Finally, this information should be helpful in filing your small claims (conciliation court) case in Minnesota:
I hope the above information is helpful.
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Thanks and best of luck!