Swallowing. Have any ideas what we can do?

Your Mom is probably on soft foods especially if she is having a swallowing problem. Like said, do not give her anything. You don't mention she has Dementia so she understand why at this point she cannot have "real food". Actually, the pudding maybe better than the "real food" served in hospitals.

From your profile:

I am caring for my mother, living in a nursing home with age-related decline, anxiety, arthritis, depression, hearing loss, heart disease, incontinence, urinary tract infection, and vision problems.

Unfortunately, you can't 'do' anything Deb. Your mother is being treated in the hospital with what's likely aspiration pneumonia so please DO NOT give her any foods that she likes to eat. The staff is aware of the fact that she isn't happy about the food they are offering her, but those foods are what her body is able to process NOW, at this stage of her disease process. Allow the staff at the hospital to treat her properly so she can hopefully heal and go back to her normal lifestyle in short order. If you give her the wrong foods, she can inhale (aspirate) them and get VERY sick very quickly. As long as she's getting fluids, even via IV, she doesn't need very much food to stay alive right now.

Sending a prayer that all turns out well for your mom.

There are plenty of "real foods" that are soft and easy to swallow - you've already mentioned mashed potatoes but oatmeal, creamy soups, sweet and savoury custards and scrambled eggs or milkshake thick smoothies are some others. But none of that is going to satisfy if she's wanting fries and a burger, have you asked her what exactly it is she wants?

Depending on what kind of pneumonia your mother has will determine what she can now eat. Like freqflyer stated below if she had aspiration pneumonia that is often deadly and she may now need to eat only pureed foods along with thickened liquids.
I would get with her doctor and see what they recommend for her diet going forward, as you certainly don't want food or drinks going into her lungs as with aspiration pneumonia.
My late husband after almost dying from aspiration pneumonia, had a PICC line put in his upper arm where all his medications were put through until he once again could swallow without danger of food and drinks going into his lungs.
He did however have to eat only pureed foods for quite some time until he graduated to just soft foods, and I had to thicken his drinks with Thick It, until his death in 2020.
Best wishes to you and your mother.

dspd77, does your Mom cough after eating "real food"? If yes, it could be she has "aspiration pneumonia" and what happens is the food goes into her lungs which causes the coughing.

The hospital staff will figure out a way to get medicine into your Mom. Usually one method is to hook up an IV solution to which they can insert meds via needle into the IV.

Oh, you still have time to remove your real name from your posting [30 minutes from posting], it is not recommended that person ID be used.