By April, it's already hot in Delhi. The best months for travelling to DEL are between mid-Nov and mid-Feb. May is hotter rt and June, just about the hottest. July and August used to be not as hot as June hot but more humid and thus quite oppressive when it's not raining. The only advantage of June is that there are fewer mosquitoes as it is too hot even for mosquitoes. The least oppressive mode of transport for the children would be an air-conditioned car rented with a driver.

Even in April mid-day outdoor activities would be taxing, but with persistence you could manage for a few days. Unless you are arriving in Delhi well rested, day one should be spent at leisure. Day two and three could be spent doing the Golden triangle, covering Agra, Fatehpur and Jaipur. Delhi is full of historic sites, but none quite as famous as the Tajmahal.