First apply for an Ipass here
https://www.getipass.com/
Mine is set to $40 max. When it gets down to a certain dollar amount they bring it back up to $40 automatically. It is good wherever Ezpass is accepted.
Register your car(s) and MH to your account. Over the years I have had; a car, truck & TT, a class A & toad and now a class C & toad registered. The transponder is in the window of the lead vehicle.
My camper plus toad are charged $4.55 total at the Rockford, IL toll as I drive right by the cash pay booths. I normally get off at I39 (no tolls) when heading south.
I did your trip a number of years ago. East coast tolls are pricey. I would suggest taking 151 to Madison. Then I39 all the way south to I80 (no tolls, maybe one). Then east on I80. That would bypass Milwaukee and Chicago. It does add some extra miles though.
If you take I43 south to I94. You want to make sure you get on I294 to bypass the heart of Chicago. A nunber of tolls with this route.
I took I80 all the way to Cleveland and then followed I90 east. I stayed at Sampson State Park In the Finger Lakes area. Nice park but your pet had to have written proof of rabies vaccination when I was there.
Have a great trip.