> knowing that the IRS flags everything over 10K

This is false.

Just deposit whenever convenient.

> thus she was sure to leave us the money in two parts instead of one lump sum check.

Presented checks are recorded in bank statements. There is a record of the transaction whether it's a $3000 check or a $8000 check. It doesn't matter whether they are deposited separately or together.

Note: If your bank doesn't allow you to deposit more than a certain amount per day through mobile phone, splitting the checks won't get you into any trouble. Checks aren't physical cash and are recorded regardless of amount.