S.H.
Your Doctor should be telling you the best options.
If you expel naturally, not all the tissue may expel either and you will need to have a D&C... a D&C ensures that all the tissues are taken out. Thus, less likely hood for infection/complications later.
I had a miscarriage once, at 6 weeks. I had a D&C. It was done in the office, and I went home afterward. Then rested.
For me, I did not want to see what came out. At 6 weeks, it is not a "baby" per say... just very tiny like a gummy bear (please excuse the metaphor) but that is how my Doctor explained it to me. It will mostly look like tissue (like a heavy period)... not a discernible "baby" per say.
You need to do what is healthiest for your body... even if you expel naturally, you need to have a follow-up... to make sure all the tissue was expelled.
I would not delay a D&C if that is what you need.
For me, the procedure was like menstrual cramps. Not real painful. And it was quick.
After I had my D&C.... my Doctor recommended not trying for another baby for about 3 months, so my body could heal. After that, I did get pregnant again, fairly quickly about 6 months later, and I now have my son!
Consult with your Doctor... and see what is best. If you must be in the hospital when your Parents are here, then that is what you need to do. Unless, your Doctor can delay it until they leave. Ask your Doctor, that is the only way to decide.
All the best,
Susan