What is the limit on reimbursement of indirect expenses due to attending conferences (e.g., baby sitting, winter coat, etc.)?
The usual solution is very simple: you will get a daily allowance ("per diem"), which is a lump sum of money that covers all small costs related to travelling.
A concrete example: a researcher at a Finnish university, travelling to a conference in Germany. You will get a daily allowance of 61 euros per day, tax free. This should cover food and all other small expenses related to travelling.
Direct costs related to travelling (conference fees, hotel, transportation, etc.) are covered based on the receipts. However, lunch & dinner is not covered, as they are included in the daily allowance. Corner cases have special rules (e.g., what if lunch & dinner is included in the conference fee).
Usually, if an "indirect cost" will be reimbursed by the university, it must be a cost that would normally be allowed if it weren't occurred on travel.
So, for instance, something that would be considered an "equipment" purchase—such as a battery for a laptop to replace one that dies—might be allowed, but babysitting costs might not.
However, most institutions do have a "travel manual" or regulations that cover what costs are permitted for travelers to have reimbursed. If you have any questions about the policy, you should consult your institution's travel office for guidance. (These regulations often change, usually in response to someone else going overboard and exploiting loopholes in the regulation, which are then tightened for everybody.)
My instinct, however, tells me that such policies are probably quite rare for any institution that accepts government financing for its operations. Usually, those funds have significant restrictions on what sorts of expenses can be associated with travel, and thus it's easier to adjust the institution's policies in accordance with that. For institutions that are privately financed, it's a lot easier to institute policies that are more liberal. But you'd probably have to go to an extremely "progressive" institution (maybe a Google?) to find one that will reimburse you for these sorts of costs.