Unfortunately, there aren't many cars that would meet all those requirements under Rs 13 lakh. You could increase your budget and get a more premium offering, or be prepared to sacrifice a few things and stick with your budget. 

Within your budget, your two best bets are the Nissan Magnite and Renault Kiger, which both offer exceptional value for money. They come with 1.0-litre turbo petrol engines and smooth CVT auto gearboxes, and if driven carefully, can deliver good fuel economy. Their touchscreens are decent but not great, and it's a similar story with their audio systems; neither gets a sunroof. 

The Hyundai Exter and Tata Punch facelifts are more affordable but not spacious enough for five, and get clunky AMT auto gearboxes. 

The Tata Sierra is the most spacious and comfortable option here, and it also has a punchy turbo-petrol engine and a feature-rich cabin. The Honda Elevate is a good option too, with a refined naturally aspirated petrol engine and a smooth CVT gearbox. But does not have the tech or space of the Sierra. 

The new Renault Duster will soon be launched in India, and we will get a first glimpse on the 26th of January. The Duster is a strong brand name and is definitely worth waiting for, so we would advise you to halt your purchase a little while longer. 

We would recommend a three-row vehicle, as there are very few cars in which the second row of seats folds flat or can be removed. Two cars in which you can remove the third row of seats to liberate a large flat area are the Renault Triber and the Citroen Aircross X. 

Both are great options that offer comfortable rides and great space efficiency. The Aircross X is larger, more powerful and from a segment above, but the Triber is more affordable. Also it has a lower boot lip height, which will make entry and exits easier for your dogs. 

All things considered, though, the best all-round option for you is the Kia Carens Clavis, though it is more expensive than the aforementioned two. Not only is it a much better-rounded vehicle with more powertrain options (including an EV), it's also the most practical. 

It has a flat folding third row, which on its own frees up lots of space. Moreover, if you need more still, the second row will fold near-flat in the 7-seat version. You should be able to fit a mattress for your dogs with a bit of folding.

The recently facelifted Renault Triber and upcoming Nissan Gravite are both good options for your usage. Essentially the same car under the skin, they are surprisingly spacious given their sub-4m length and overall size. 

The advantage of getting a 7-seater in this case is that, for your occasional 6-seat use, you will be able to manage with this car, and for the rest of the time, your 4-5 passengers will be more comfortable, and you can carry some luggage too. 

As a commuter, its compact dimensions make it easy to manage around town. Renault and Nissan's quality and reliability have come a long way since the early days. Though not quite up to the gold standard of certain other brands, are not a serious issue in the slightest. 

The Punch EV is a good choice, too. But for the reasons mentioned above, as well as your 1,500km monthly usage, we'd recommend sticking to a 7-seater and an ICE vehicle.