Yes, but if you know your son is a weakling and unsuited for the job, then I think it is only natural to try and influence things. Firstly to save the country, and secondly to stop him making a fool of himself, and embarrassing the family. More so, when you know his wife is also incompetent and unsuited to her position.
I think any mother would have done the same. If I was in the same position as her, I would would have interfered hugely, rather than sit around doing nothing. At least Alexander lll was a strong Emperor and did not need any advice from his wife. So I dont think one can compare the two. Its a pity he did not absorb the advice he was given by his mother and uncles, and applied the best of it. Perhaps it would have been helpful in the end.
As for using state money to bail out her friends. Lucky friends. Most members of the Russian Royal family abused the system anyway. The Emperor had carte blanche, and would hardly refuse his mother anything. I am sure this went on all the time.
After all, everything belonged to them.
Read Catherine the Greats Biographies, if you want to see abuse of state monies !!