Qasr (Shortened Prayers)
Traveler must pray his prayers as Qasr as far as his travel is lawful. If he forgets and prays full, he needs to repeat the prayer which was wrongly performed.
As you travel every day for work, you must perform you Salah as full in both places, your home and your work place. Every one who travels for work three days a week or more, his Salah is full.
Yes, this is allowed...
Yes it is permissible to pray behind a person who is praying Qasr, if all other conditions of Salat Al-Jama'ah are met.
If you have another option to pray behind a person who is not a traveler, then such option is better for you which means more reward.
If the traveler is praying exactly behind the Imam of Jama’at, those who pray on his right and left will remain connected with Imam because they are near the Imam, and others who are connected to them will remain connected as well.
If the traveler is praying in the first row away from the Imam, on any side , and he finishes his Salah, those who are away from the Imam will be disconnected if the gap is more than one yard. Many scholars say that one person does not make disconnection, but Ehtiyat ( precaution) is always good. Travelers should not pray in the first row. If they pray in any other row, they will never cause disconnection to others.
Even if disconnection takes place, the Salah will remain valid, but not as Jama’ah but as Furada just after disconnection.
Since you will stay over 10 days, you will pray full
She should do qasr.