Maybe bite the bullet and take it to an established detail shop and let them deal with it...
Otherwise, rubber gloves t start with and use paper towels to scrape or wipe off as much of the solids as you can and dispose of ASAP
The you can try to use an upholstery cleaner or a fabric safe All Purpose Cleaner but seriously, if it were mine I would locate an established detail shop and just pay someone with an extractor to do the work for you.
Since this is your first post to our forum...
Welcome to Autogeek Online!
Hope you're dog is doing okay...
:xyxthumbs: