I'm at the point of no return, but by siding with the BOS what is the fate of the Minutemen? If I can continue with the Minutemen after destroying the institute will they ask me to destroy the BOS?
If you continue down the path with the BOS, you will technically ally with the Minutemen.
From the Fallout Wiki:
Brotherhood and the Minutemen allied - with the Brotherhood's new Sentinel being none other but the Minutemen General, the two factions are technically in alliance
If its not clear from the quote, you are promoted to the Sentinel rank in the BOS after completing the game with them. Since you are also the General for the Minutemen, you are technically now allied with the BOS, though I do not think there is any official ruling in the game saying you are.
After completing the main quest line, you can go back with the Minutemen and take out the BOS:
Brotherhood of Steel gets betrayed and destroyed by the Minutemen - should the player become hostile to the Brotherhood after the Main Quest is completed, the player can ask the Minutemen to help them destroy the Brotherhood, just like in the Minutemen ending
Note that this is only if you become hostile with the BOS after the quest for whatever reason.
From personal experience, I finished the game with the BOS, and now the Minutemen and them coexists peacefully. Should I choose to one day destroy the Brotherhood, I can still do so. I suppose there is nothing stopping me from taking the Minutemen out either.