No, you have not been doing things "all wrong."
You apparently have live, healthy chicks, so you have done a lot RIGHT.
So you have the young chicks at 2 weeks old, and two at 19 weeks old, and no other chickens?
If you want one possible sequence of moving your chicks outdoors:
--Leave the chicks where they are for now, until the weather next warms up.
(so they are in the garage, with heat lamp and additional heater.)
--As soon as the weather warms up a little bit, like up to 50 at night instead of 40 at night, turn off the additional heater in your garage. That would still leave the chicks with the heat lamp.
--A few days after that, start reducing how much heat the chicks get from their heat lamp. You can do that by raising the heat lamp, by moving the heat lamp further to one side or end, or by using a smaller bulb in it.
--I would try to have the chicks at the point of NO additional heat, but still in the garage, by the time they are 4 to 5 weeks old (or sooner, if they seem comfortable. Just watch how they act: happy contented chicks are fine, but huddled peeping chicks may need more heat. Chicks that are scared because you just moved the lamp will also huddle and peep, so wait at least 15 minutes for them to get used to a new situation before you decide they really need more heat.)
--Somewhere during the time you are reducing heat in the garage, I would start taking them outdoors in the daytime. Since you have said your weather is quite variable, just start with a day when the outdoor temperature is higher than whatever the brooder temperature is at that time. Gradually increase how long they spend outside, until they are spending all day outside no matter what the temperature is.
--once they are comfortable outside all day, have them spend the night outdoors (in the coop) as well. Watch the weather, and pick a night that is not extra-cold.
--a wire mesh divider can let the chicks start getting to know the adult chickens, but without any danger of getting pecked or bullied. Or they can spend their outside time in a pen next to where the big chickens live.
--once the chicks have been seeing the adults through the divider for a while, switch which birds are on which side of the divider. That lets the chicks explore all parts of the coop & run.
--When the chicks seem comfortable in all areas, try letting the chicks and adults be together. Watch them, in case you need to do any rescuing. But with only have 2 adult chickens, I think you have a good chance of getting them integrated quickly and easily. The temperaments of your adult chickens will have a BIG effect on whether this works, but of course you won't know how they react to chicks until you try it.
--if the adults are fine with the chicks, make sure there are several sources of food/water/hiding places, and leave them together. Check carefully at roosting time, until you've seen them go to bed properly for several nights in a row.
--if the adults are not fine with the chicks, consider making chick-sized openings in the divider, so the chicks can choose to mingle with the big birds but can easily escape when needed. That lets them integrate at their own pace.
There are MANY other ways you could progress to moving the chicks outdoors. This is just one option.
Here is another approach, that involves raising the chicks in the coop:
https://www.backyardchickens.com/articles/integrating-new-birds-at-4-weeks-old.72603/