I'm at the cross roads on this myself.
Originally my PC felt that she would do anything to find out what happened to her son and all fingers pointed to the evil institute having kidnapped him. So she did what she felt she had to in order to track down the Institute. She sided with the minutemen, then the Railroad and eventually even got tangled up in the Brotherhood of Steel.
But then it all fell apart. The Railroad helped her get into the Institute where she learned the truth. Or at least a sugar coated version of it. But nothing about them seemed as evil as the outside world would make them out to believe. She soon realized that just as the Institute had a shallow and sheltered opinion of the outside world, the exact thing could be said in reverse. Everyone on the outside had no understanding and feared the Institute because of that lack of understanding. She saw scientists working freely with each other in stimulating research labs. They even had families living with them.
And that is when her alliances fell apart. First was the Brotherhood of Steel. Trying to play both sides to find a peaceful solution, she had been working with the RR and the Institute in jobs that sort of helped neither side. Kill a Courser here, retrieve a synth there... But then the BoS showed up and began shooting everyone at Bunker Hill. Synths and RR agents alike. So she took a stand against the BoS and when the time came she officially waged war against them and made them the enemy.
But now I'm back to the crossroads. The middle has been traveled for about as far as it will go. With the Railroad, she took out the BoS officially after the BoS came after the RR hideout. The only BoS left are those on foot headed back to the Capital Wasteland. But the Institute wants me to kill Desdemona who does not seem interested in trying to find peace. in fact she wants me to help her blow up the Institute.
I don't want to make an enemy of the RR and kill them all after recording a message of peace for the commonwealth. But I'm thinking a shot fired from a silenced gun from a darkened corner is waiting for Desdemona. There is no justification for destroying the Institute when there is so much potential there that can be used for the betterment of mankind. And with me as the director of the Institute... anything is possible.
So who to side for? That's up to you. Its been a tough decision for me. but on this round, Institute it is.