Hi @Chrisguff12 :
Do you want to email the filtered table to the specified user?
If so,I'm afraid this is a bit difficult.The key is that you need to convert the table into HTML format, but PowerApps does not provide this feature. My suggestion is to insert a flow.I've made a test for your reference:
1\My data table:
ClearCollect(QQQ,{ID:1,ColumnA:"1",ColumnB:"2"},{ID:2,ColumnA:"1",ColumnB:"3"},{ID:3,ColumnA:"2",ColumnB:"2"},{ID:4,ColumnA:"1",ColumnB:"2"})
2\Create a flow('PowerApp->ParseJSON,CreateHTMLtable,Sendanemail(V2)')

Note:the Schema parameter is depends on the schema of your data source.If you don't know what it is, you can automatically generate it by clicking ‘Generate from sample’ and entering the JSON of your table.
3\Insert this flow into your app

4\Add a button and set it's OnSelect property to
Set(TheTable,JSON(QQQ));
'PowerApp->ParseJSON,CreateHTMLtable,Sendanemail(V2)'.Run(TheTable)
On your side the code should be
Set(TheTable,JSON(Switch(
'Date_Filter_VH-C_Dropdown'.Selected.Value,
"This Week",
Filter(Etcher_Cleaning_Sheet,'Date and Time'>=DateAdd(Today(),If(Weekday(Today())<>1,-Weekday(Today())+2,-6),Days) && 'Date and Time'<DateAdd(Today(),If(Weekday(Today())<>1,9-Weekday(Today()),0),Days)),
"This Month",
Filter(Etcher_Cleaning_Sheet,Year('Date and Time')=Year(Today()) && Month('Date and Time')=Month(Today())),
"Year to Date",
Filter(Etcher_Cleaning_Sheet,Year('Date and Time')=Year(Today())),
Etcher_Cleaning_Sheet
)));
'PowerApp->ParseJSON,CreateHTMLtable,Sendanemail(V2)'.Run(TheTable)
The Result:

Best Regards,
Bof