Joining prayers in a care home

Asallam alaikom wa rahmatullahi wa barakatuhu, This question is regarding joining prayers in a care home. I am a female, UK, and I work at a care home for old ladies who are sometimes bed bound and helpless, they need medication at certain times and personal care, personal cleaning and bed pans etc . Often there are emergencies where the old lady suddenly loses ability to walk or they have dementia. My shift is between 4pm -10pm. With consecutive 30 minute windows between each ladies flat in the building, I do not always have a break. My colleagues are often rushing around and it can be fast paced. If I manage to find time to pray, it takes me 30 minutes because I have to remove my najasa clothes and wash and then change into clean clothes, make wudu and then go and pray 4 rakats without Quran and then change back into my uniform. The whole place is not clean because they have accidents on their chairs and on their carpet. I am observing proper hijab at work wearing lose clothes, everything including a clean hijab need changing and I cannot be late to any call. These days I have been joing dhuhr and asr before I go to work and when I come home at 11pm, I eat, wash and then join maghrib with isha. Is this permissible ? JazakAllah Kheiran for reading from me.