Transportation can be a challenge in Glacier. If you have ideas, offer ride shares, or used a commercial service that you were happy with, let everyone know. Also, ask questions about road information, or share road information you may have.
If you get there early (let's say by 8:30-9:00am), I don't think parking will be an issue at Two Medicine. However, on July 4th I'm not sure Dawson/Pitamakin loop will be passable due to snow field challenges. Others here on the chat page might know the conditions better. Also you can check the trail status report online.
We are in the mountains and the mountains are in us. - John Muir