You could contact Comfort Inn and Suites on Macleod Trail and ask them too. When I've driven by there, it has not seemed to me as if the property has had lots of parking. It's on the side of a small hill. It's possible that the parking is underground. If that is so, I doubt that they'll be able to accommodate your trailer. But it's worth asking.
You also could ask the Holiday Inn at 4206 Macleod Trail. Their website says they have three suites. They have open air parking, so perhaps they'll be able to accommodate your trailer. I would ask, just to be sure.
Probably Holiday Inn Express Hotel & Suites Calgary-South at 12025 Lake Fraser Drive SE would be able to accommodate your needs, but it's further away from downtown than the other two properties I mentioned. It's a 15- 20 minute drive in off peak hours, I would guess 30 minutes in rush hour.
There are quite a few suite hotels in the northeast quadrant of Calgary, and those hotels usually have complimentary parking. If you do a Google search, you can identify those hotels from the fact that their street addresses end in NE, and they often have the word "Airport" in their name. They are further from Stampede Park, however, so I regard them as "Plan B."
Hotels in Motel Village, in the northwest quadrant of Calgary, usually provide complimentary parking. But, from what I've seen, their parking facilities are not as large as those in the northeast quadrant. That is, I suspect the properties in Motel Village would be more inclined to impose a one parking spot per room policy. (I'm guessing your trailer and the vehicle that pulls it will essentially occupy two parking spots.)
You will need to avoid any suite hotel that describes itself as being downtown.
Hope that helps.