Some questions still remain
Dinosaurs had more or less the same sort of genital arrangement as do birds, namely a common orifice for urine, faeces and genital systems; this set-up is common to birds, reptiles and marsupials. Only eutherian mammals (the group we're in) evolved away from this arrangement.
In reptiles, this makes mating a fairly delicate operation; the male has to get it just right although having not one but a pair of penises probably assists somewhat here. In birds, a couple of different techniques are used; the majority use a penis-less sperm transfer, and ducks, geese and ratites use various penis-like structures of varying but occasionally rather improbable dimensions (two feet for Argentinian Lake ducks).
Dinosaurs presumably used penis-like structures and some seem to have slightly more robust pelvic bones that presumably acted as support. However even this arrangement still looks improbable for animals like Stegosaurus; the dorsal plates would seem to preclude the male getting very close to the female. Stegosaurs also had particularly small brains, even for herbivorous dinosaurs, so whatever they did must not have required much thinking to achieve.
The only problem is that behaviour and soft tissue structures don't fossilise. So, any suggestions as to what went on?