You could try this:
df.to_html(classes = 'my_class" id = "my_id')
It's like a SQL injection basically.
Pandas' to_html function uses double quotes around the class. You can use single quotes to define the classes argument, and put double quotes inside them to end pandas' class. Then put opening double quotes around your id name but let pandas' close those double quotes for you. The output will be the following:
'<table border="1" class="dataframe my_class" id = "my_id">...'
Hope that helps.
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