of Mitt washing the family pet ...

is going to be routine maintenance for the life of that washer.

The only filter my old Kenmore has is when I put a piece of stocking over the end of the drain tube to catch fiber when I process raw fleece in it.

The only other thing I can suggest is buying a Velcro pet hair brush and getting rid of as much of it as possible before things go into the washer. Then maybe you will only have to pick it apart once a year.

and run it on the no-heat fluff setting for 10-15 minutes.
It will be MUCH easier to remove the dog hair from the drier filter.

As someone who lives with a Shedding Team of two dogs and two cats, one of the dogs being half American Eskimo, I commiserate.

My newest one thinks are his.