Sorry it is not possible to open the filter button with a custom button because these are functional buttons and it is now possible to replace them with the custom button.
If you want to change the icon etc of the filter button it is possible with custom css. If you have any questions feel free to contact us.
Please deactivate all the 3rd party plugins and activate only theme-required plugins on the site and then check the issue. I am sure your issue will be solved. Then Activate the 3rd party plugins one by one and check which plugin is creating the issue for you.
Otherwise, if the issue still exists then keep the 3rd party plugins deactivated and let me know I will further check on your site and give you a possible solution.