B.M.
You can't make it work without a court order. Those "stings" are called protection. If you don't want them.... there are consequences to that, as you are finding out.
If you don't have a court order... then his is not LEGALLY ordered to pay one damn dime and he can do as he pleases.
If you don't have a visitation schedule he can see her when and how he pleases.
As far as driving on one weekend to see him.... that is small potatoes compared to the big picture. You're focusing on the details, because it's easy to quibble about who drives when and what is fair. Instead of that... get yourself a court order for both visitation and child support, lay out who is responsible for what and deal with the bigger picture.
If you don't want that.... then get yourself some "strings" that offer some structure and accountability.