I do not like to use owner-direct rental sites like VRBO and AirBnB for apartments in Italy, due to all the uncertainties and possible things that could go wrong. Just yesterday there was a trip report by someone who rented 3 different apartments in Sicily on AirBnB. One was outstanding, one was average, and one was truly awful.
I have used booking.com to find apartments in Europe; they are still owner-direct rentals, but booking.com provides an intermediate layer for security and a good platform for communication and problem resolution. Plus you pay by credit card, so there are no worries about getting cash to pay, or wiring money directly.
For Venice specifically, I only use a local company named Views on Venice. They are reliable and professional, and have provided excellent service on the occasions we have used them. They have apartments in both Venice and Florence.
Here is one example of an apartment in Venice that would sleep your family comfortably and is in a good location ( note that the price for your actual dates may be higher than the €235 a night listed; I booked it for September high season and it was more like €300/night)
https://www.viewsonvenice.com/rentals/apartment-venice-la-tana-278123.html
Here is their main website so you search for other options. There may well be 2-bdr. Apartments that are lower in price than this 3-bdr.
https://www.viewsonvenice.com/
Note that they may not have many listings yet for April 2024, which you mentioned as trip dates in your other thread.