These are both domestic flights, so this is straight forward enough.

It appears that Akasaa and Vistara are not interline partners. That means you have to collect your bags on arrival in Mumbai, leave the secure areas and drop them off at the Vistara bag drop or check in counter in Mumbai and then clear security again. 

Think about it as two separate flights. The steps that you have to go through are the same as if you were flying on two separate days. It just so happens that arrival from flight 1 and departure of flight 2 happen on the same day and you are not doing anything else in Mumbai in-between, you are just staying on the airport.


If things go reasonably well. 3.5 hours should be fine for that. Vistara check-in closes 1 hour before departure for domestic flights, so you have over 2 hours to get your bags and make it to the counter. So unless there are any major delays or hiccups (lost bags) that should be ok

>  but my first flight from Ahmedabad to Bombay (Akasaa airline) got cancelled

As this was originally a single PNR, Akasaa is technically on the hook to provide alternatives. Did you explore this with them? What are they offering as alternative routings and/or compensation/refund.