Hello amy45,
I know how important it is to select the proper taxes on your expenses. Setting up new tax codes is made simple in QuickBooks Online. I'll help point you in the right direction for help with your M&E tax defaulting to HST ON tax.
First, ensure you've set up your custom tax code according to these steps: How to set up a new sales tax code.
If you've done that, ensure you're selecting your new tax code when you select a tax from the Sales Tax drop-down menu on your transactions.
In this case, the solution will largely depend on how you've set things up and how your specific account information is appearing. I recommend reaching out to a tech support agent so you can get the best guidance on how to fix this. The agents on the phone are able to do a remote screen share session to see exactly what you're seeing and get you back on track.
I hope this helps.
Have a great weekend.