Hello, our nearly 3 month old is trying to roll back to tummy in her bed and sleep, and is getting close but she has only succeeded on getting to her side yet. Should we unswaddle her? It’s hard because her arms are still shaky. Also she sleeps in a co-sleep bassinet but she’s rolling her face into the sides, but her big crib is in the other bedroom as it won’t fit with us. What is more important moving her to the big crib or having her in the same room as us, we can’t do both?

Now that your baby is rolling it is important that she is no longer wrapped/swaddled & she is moved from bassinet to cot.
She needs her arms free & the space of her cot to roll safely.

A safe environment takes priority over room sharing if both are not possible.
Parents are not expected to observe their baby constantly. If your baby is sleeping in a separate room check baby regularly to ensure that the baby remains on the back and the head and face remain uncovered (as baby grows beyond 5-6 months they will move around the cot and roll over; settle baby to sleep on their back but let them find the sleep position they feel most comfortable in. A safe cot and safe sleep environment is still necessary for babies older than 5-6 months).
https://rednose.org.au/article/room-sharing-with-baby

Most babies will be rolling over by 4- 5 months - some earlier. This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their side &/or tummy.
This is not something that needs to be stopped. It is important to make her new environment as safe as possible.

Ensure that the cot mattress is firm & flat & there is nothing soft or loose in her cot
You can try to turn her back, but often, babies will just go back to their position of comfort.
Always continue to place baby on back to sleep.
Increasing tummy time when awake is also helpful.

Red Nose has the following information now that your baby is starting to roll.

Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over