Yellowstone or any other place in the Rockies can have (at times) equally inclement weather in the summer. I grew up in Laramie, WY and have seen snow there (7100 ft.) in July. Of course Yellowstone is at a slightly lower altitude than the Wind RIvers. It is also much less scenic, has stinky hot water and lots of bears that are not afraid of people. Personally, I would take the Wind Rivers over Yellowstone any time. Of course, as you can tell from my description, I don't particularly like Yellowstone! I used to go there every year, and after a few hours I always wanted to leave and go to the Tetons or some other more scenic locale.

Backpacking in national parks requires permits, which often have to be obtained months in advance. You can't go where you want and camp when you want. You have to adhere to a rigid schedule. If you get a blister or find a beautiful camp site and want to stop early, that's too bad--you have to camp where your permit says. For this reason alone I'd recommend staying outside of national parks where you can be far more flexible.

Wherever you go, I suggest you plan your trip on established trails in more popular areas. Going into isolated areas or off-trail is not something I would recommend to a beginner.

The main thing is that you should do lots of practicing before you leave home. Not only should you be doing lots of walking (preferably with a pack) and climbing lots of hills or stairs or a stair-stepper or inclined treadmill every day to get into shape, you should practice setting up your tent, cooking and sleeping out in your back yard multiple times in all kinds of weather, long before you leave home. You need to learn these skills before you get out on the trail, no matter where you go. As I mentioned earlier, the next month, before warm weather arrives, is an excellent time to test the limits of your gear. Not in a blizzard, but when it's at or below freezing and in wind and rain.

No matter where you go, plan your trip so that you visit your mom first. You should spend a few days before your hike to start getting accustomed to the altitude. You should also plan to take it easy the first few days of your hike.