Self-Driving at Kruger National Park: Are there rental car services in or near the park?

My family and I are ecstatic about our S. Africa trip next year. We are on a tour bus company (Expat Explore), and we have three free days at Kruger National Park (not nearly enough!). We have questions about the feasibility and practicality of self-driving in Kruger (in the interest of saving money for our family).

I know that the Park's hours are 6am-6pm, and in order to see the animals at their most active, you have to go on a Dawn & Dusk safari tour with a trained guide. We will be doing that.

However, during the daytime.... we still wanna explore this massive and beautiful park. I know there are safari packages for the day, but they are far above our budget, and we read that it was cheaper to just rent your own car and drive yourself than pay a safari (where you'll be crammed with strangers, on their schedule, and not the best visibility in a long van where windows don't open).

Are there rental car places in and around Kruger National Park?? Our Bus Company takes us and drops us off West of Kruger at our accommodation Bundu Lodge in Nelspruit (and I believe they just assume everyone will pay for the safaris -- even in the day), but I read that self-driving is much cheaper and preferred -- I just don't know if these comments I've been reading are from people living in South Africa or rented a car much further out and drove them into the park...

Can one just rent a car when they get to the National Park? Are there a few companies in Nelspruit area? Preferably, nearest to Bundu Lodge?? Since we'll be without a car (and there isn't public transportation that I know of), we will probably have to walk to the nearest rental place from Bundu Lodge.

The roads, for the most part, are paved or have dirt roads that are free of rocks, etc., right?