I sort of agree, weirdly. Funerals are weird, OP, as is family. As someone with a horrendous family and a very bad social brain, I totally empathise with saying you have ‘no bandwidth’. But you only get one father, and one funeral for him. This need not be a long and drawn out event.
In your position, I’d tell him you’ll go and you’ll have a shitty time and you’ll really hate it and let him know you’re doing it for his sake. That way you’re not lying, you’re just agreeing, in the worst case, to waste a few hours of your life with some unpleasant people.
Even better, tell him you want a nice time out now, like a nice dinner, as payment for enduring his funeral when the time comes.