1) If you are not driving / rental car, I'd suggest to stay at Iron Blossom (Snowbird) or slope side lodgings at Alta.
2) Consider to give UTA bus a call, ask whether or not bus can stop at Hellgate condo.
3) Can you call Hellgate to ask whether it is possible to get to Alta by taking UTA bus? I am sure you won't be the first guest asks this question.
4) My 1st time visit to Alta, I stayed at Iron Blossom and skied Alta. I did not have rental car. I took Canyon Transportation from SLC airport to Iron Blossom. I remembered I called them to see if it is possible to stop by grocery on the way to Cottonwood. The answer I got was, they can if other passengers don't mind the short stop. There is also a shuttle takes guests to grocery every Wednesday evening, I don't know if they (Iron Blossom or Canyon Transportation?) are still doing it now.
5) I've been to LCC few times and remember seeing Hellgate condo on my way to Alta. From what I see, it's not an easy walk to and from the property. I don't see sidewalks for pedestrians.
6) For your lodging options, may I suggest 2 alternatives?
i) Gold Miner's Daughter Inn. Some folks prefer it since it has an elevator and TV in rooms. It does not require rope tow to get to the lodge. It is located in "front" of Collins Lift. It does not have minimum night stay requirement. It is a true ski in/ ski out lodging.
ii) Alta Peruvian Lodge. I stayed there first time in December, 2020. I liked it enough to be my first choice for lodging in Alta slope side. Location wise, it is not as close as Alta Lodge or Goldminers. It is located across the parking lot, an easy walk to get to slopes, ~3 mins walk to Collins lift / Wild cat base area. Rate is included 3 meals. Only issue is you mentioned about food allergy. You can visit their website and check out menu (to get some ideas).
Since you are going in later season, I don't know if you can do ski in / out.
During mid season, it is possible to ski out, there is a groomed trail just for that; ski in - access from Wildcat chair. Again, you can call staff and ask if you want to know more. I found the staff there to be friendly and approachable. I asked all these questions when I stayed there in December.
They also have an outdoor hot tub (which I prefer). Early April will be perfect to stay out.
7) Check Hotels.com for lodging at Alta.
I keyed in early April dates and this is what I got for 1 person at Alta Peruvian. You get a bunk bed room, bathroom in room (not shared). Since it is COVID year, they are not putting you with someone else. If you are traveling yourself, you get the room yourself. I understand you are traveling with your son. When I keyed in for 2 person, hotels.com gave me a different room with >2x the rate.
This is what I would do (if proceed w/ this booking), book the room from Hotels.com and key in 1 person. Then call Alta Peruvian and explain your son will come along, so you two will share the same room. That way, they will charge additional person at the same nightly rate and put you both in the same room. But you need to do this through Alta Peruvian, not hotels.com
I know this because I asked this question in December (since I was considering a return trip with a friend).
8) As for COVID protocol, at Alta Peruvian restaurant, there is no menu, I use smartphone to scan a QR code, it took me to menu and I select from there.
I took few photos (including food pics) when I was there. I can post here if you want to see. Alternatively, you can check their website for photos.
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