Put the cat and dogs in a Carrier, take the top off and fabricate a rack for upstairs and put the travel bag on it as well as some of the other stuff.
Get carriers at st vinceint de paul or goodwill. cheap
don't want a cat running loose inside anyway. you will pay for it, cat and dogs will be happier. Just stop every so offten to let them go tinkle. Watch out for the cat, will want to run away. Or give the cat away (mom or Sister).