I agree with Christy Lee: It's time for mom to change the pattern of *how* she deals with soothing her little screamer.
It's good that this is being addressed now. I have seen it go on into a child's threes and some actual developmental damage had to be undone. Mommy did so much for that child that the child wasn't developing the physical coordination skills appropriate for their age. (Oh, heavens, that was a whole other hard conversation with that parent!)
Here's what I would do:
Start re-training the child's expectations.
Child cries. Mom says "I'm doing X. I'll pick you up in one minute." Put a timer on if need be, mom finishes quickly and then picks the child up and verbalizes "Now *I am ready* to pick you up." This will need to be repeated for a long time. These words tell the child that they must wait until MOM is ready.
If the child begins to cling, get underfoot, or otherwise prevent Mom from doing her task, use a containment device, such as a stroller or high chair. (Be sure to buckle up the child with a 5-point harness at this age, esp. when they are tantrumming.) "You may play here. I am busy. I'll hold you in a few minutes." I did this with my son quite a bit when he went through clingy phases and wanted 'uppy' while I was needing to make dinner or move laundry. I brought the umbrella stroller to the door of the kitchen, set the brakes and put him in it with some toys. "You may play here. I need do my job now." Sometimes he'd cry and I'd just have to steel my own emotions for a few minutes, complete a short task (about 3-5 minutes, which is a HUGE long time for this age, sometimes) and then comfort him.
What I found is that once he was contained and I was actively ignoring the screaming/crying, it gave him time to get interested in the object I had handed to him. Kitchen items, by the way, are a great on-hand novelty distraction. He learned, slowly, how to entertain himself this way.
Start with small deferments-- just put her off for one minute at the beginning. She needs to learn to trust that she can wait for a minute and then mom *will* pick her up. Once she becomes secure in that, even if she still cries-- once that's become the pattern for a couple of weeks, then you can lengthen the time it takes to pick her up, a bit at a time.
Also, do understand that neurologically, the baby (still a baby!) and toddler brains--even through preschool age-- are developing, and that little ones sense 'loss' or 'deprivation' as actual pain in their brains, which is why they respond the way they do. This is why this is a long-term teaching of expectations and boundaries. It won't happen overnight. Be patient and consistent. And of course, if a child is hurt or sick or genuinely upset, do not put them off.
At this age, too, your girlfriend might consider using an Ergo or other backpack-type carrier. I often wore my son a LOT until he was about 2 or so. Not so safe to do while actually cooking, but I've prepped a lot of meals when he was on my back. I also think that little ones like seeing the world from our height, so when your girlfriend's daughter gets older, a 'learning tower' type stool might help a lot, or moving her high chair to where mom is working at the counter. Just a few other ideas.