Are There Taxi's with Child Car Seats in Milwaukee?

Public transportation is not required to provide car seats, same as on a bus. You should be able to contact the cab company and ask if they have one or you need to bring yours. Personally I would rather bring my own since I know it would be clean. The hotel should be able to store it for you.
Another suggestion would be to get AAA it's about $50 a year and they will send someone to jump start your car if you need them. I have had them for years and have been so glad I did. One call and it's paid for itself. Or call the hotel and see if an employee there can jump start your car should it not start.

I doubt that you'll find a taxi WITH a car seat but you can certainly take yours. I can almost guarantee that the Hyatt has a luggage room where you can stash it for the duration of the event. I doubt there will be a charge...call them and ask. I think you'll find them very accomodating.

Ok I don't know about Milwaukee, but in most cities if you call the cab company and make a reservation, you can request a car seat at that time. Usually the company will have cars in it's fleet that can meet your request.

Second option.... When you get to the hotel, you can probably check the car seat with the coat check person or at the front desk. Call the hotel in advance just to be sure.

Any halfway decent hotel will check baggage for you. Yes there is a fee, and tipping is standard.