Train the dogs to lay against the sill.
Get a hair dryer
Heat gun
Kettle of boiling water
Use the other door
Dogs aren't allowed there t night.
No other door will suffice due to what is beyond to confine dogs and clean up after them.
Frost is on the outer edges of weatherstripping. And where latch edge of door meets frame. That is far side of insulative material making heating from the inside not transferable in any brief amount of time. IF osmosis transfers enough heat through the material.
Dogs and wheelchair add to snow /ice/water tracked across threshold. Door being open allows escaping heat to heat edge of oof causing melting icicles dripping. Compounding the issue.
Pulling on the handle (this is not the first door or first handle on the same doorwall) isn't the answer. It isn't held on with enough.
Unlocking the latch first does seem to help.
Pushing on door frame mid span on the opposite side than the handle while keeping tension on the handle isn't the worst way to break the ice bond. But that has me leaning forward from a seated position and the chair dancing. Or balance on one leg standing up and stay balanced when the door breaks loose. Ya the chair works better.
Now clean the forehead print off the glass and we're all set.
Colder weather? Use a tool to remove ice from multiple usual areas while door is open and heat escaping melting what ids above it outside.
You can see the track being spread by ice build up on door. And one outside corner ice builds up fastest that will keep door from fully closing. And a gap resulting will create lots more ice lots faster!
A particular tool that worked real good I kept close. And it disappeared. No one knows anything about it...