Specifically, it's a bad idea because:
(a) As Dale said, the other members of your alliance will hate you.
(b) Your stability will plummet and BB will rise from breaking the alliance and declaring war without cause. Revolts will probably break out quickly...
(c) You are not that close to the Mughal and only have half your country to draw from. The Mughal will be defending on home terrain. Even if you manage to time it just right and smother all their lands simultaneously, they can break the siege with one of their armies returning from the south and ruin your plans.
(d) If they haven't had a war yet, they will have a huge starting army. Even if that army is gone, if it takes you too long to declare the war and get into position, they may have built a sizable army for the new war.
(e) You will still be at war with the first nation you declared on. If they can still reach you in the Mughal lands, you will be fighting them as well...
(f) You've been conquering and annexing enough that I'll bet your BB is already high. If you get into a long war with Hyderabad (for example) and Mughal then you will almost certainly get attacked on your flanks (Turkey, etc...)
On the other hand, learn by doing, I always say...
