The answer depends on the terms of the trust. If the trust provides that trustees may be added, then the trust may be amended. If it does not provide for additional trustees, then it cannot be amended. Your concern, however, may be more directed to who the beneficiaries of the trust are, and if the trust is indeed irrevocable, that is something that cannot be amended.
An irrevocable trust, by its very nature, is irrevocable and very difficult to amend.
If the sole purpose of your mother amending this trust is to add your sister as trustee to make her feel included in some way, then I will have to say that is probably not the way to go. She can make her feel included by many other ways: set up another trust, give her some other powers.
Your mother must have created this irrevocable trust for a very specific reason. It was either a medicaid trust or a tax planning trust. Unless you go see an estate planning attorney to look into the specifics and also unless if you have a very very good reason, don't touch it.
Irrevocable trusts are specifically intended to be unchangeable. Irrevocable trusts allow for specific benefits and advantages to the grantor and the beneficiaries that revocable trusts do not have, however once they are created, they are not within the control of the grantor to amend. Because of this, it is not unusual for the trustee to have the ability to make some limited changes.
You should consult an attorney in your area who specializes in trusts.
There is more than one issue here. Getting a new or additional or different trustee usually isn't that hard either by mutual agreement or by filing at the Probate Court in your county (Middlesex). The harder part is "adding your sister" but there are both legal ways and practical ways that this might be accomplished. You would need to see an attorney to help you here.