This sounds like your mother is the curretn ebneficiary during her life and then you and your sister are benficiaries after your mother passes.
1. can our Mother use funds in the trust to pay the tax? Whether or not the trust can pay for the expenses would be determined by looking at teh trust documents; but it would be very unusual for the trust not to be able to pay for the expenses related to the property in the trust.
There is usually language that lets the trust pay for whatever your mother needs while alive.
2. who decides where this cash will be invested? The trustees decide how to invest the assets of the trust.
3. Can this trust be broken up? Probably not, as you did state it is irrevocable. Satte law may apply to limit whart can be done; and again, the trust agreement would say if there was any circumstance in which the assets of the trust could all be distributed (that might be allowed for the benefit of your mother so long as it was not against state law).
4. If I invest it in property, will we have to pay the tax when my Mother dies on this money at 39.6%? The assets in the trust will get an increased basis when your mother passes so you and your sister will likely only have to pay tax on any gain after your mother's death (If i am understanding correctly the type of trust)
Should we just invest in something that generates CG? As you said, it is your mother as the income beneficiary that has to pay tax on the income. It may or may not be preferred to only invest for capital gains or it may not cost more in tax to generate ordinary income depending on the specifics of her situation. Any question that asks "should we invest" has much more than tax considerations - such as, will your mother need the cash to pay her expenses so you do not want all teh assets in real estate or other items that are not easily converted to cash; and the level of risk that is acceptable, etc. As above, this is for the trustees to decide.
I hope this general information is helpful for you and your mother.