QB Issue Resolution:

You can track all those items in QuickBooks Online.  Self employed is ideal for people who need to do invoicing, track mileage, and if you mix personal and business expenses.

If you track your business expenses separately from your personal, you can still make QuickBooks Online work for you.

Vendor would be anyone you pay money to as part of keeping your business running. This could be the grocery store, the craft store where you buy your supplies to keep the kids busy, etc.

Customer would be I assume the kids parents as that who you would be billing and collecting income from.

In the Chart of Accounts is where you specify what all your expenses are for.

Resolution for Issue 'how do i track expenses for a daycare with my Quickbooks Online account? the options are “vendor, employee and customer”, but i need to track groceries, supplies, etc' available: Yes (Solved).
Source: Intuit Community forum.

how do i track expenses for a daycare with my Quickbooks Online account? the options are “vendor, employee and customer”, but i need to track groceries, supplies, etc: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

Support for business expenses
Quickbooks Repair Pro will resolve it efficiently and affordably. Guaranteed resolution of your issue, or you pay nothing!

Error Recovery for business expenses [Canada]
E-Tech is the #1 Quickbooks data migration and Conversion service provider.

Get 50% off Quickbooks Online

Click Here for 50% off!

Additional Support Options: