I agree with the drip tape idea - it's really the most practical option for your situation. We had a similar plot when my husband and I first started gardening. Drip tape costs next to nothing (I used to buy it for 200-300 rubles per 50 meters), it installs in an hour or two right along the beds, and most importantly - it saves water three times over compared to regular hose watering. For tomatoes and cucumbers it's just perfect, because the water goes straight to the roots and the leaves stay dry.
I'd recommend getting standard drip tape with 30 cm spacing between holes, and connecting it through a simple water timer (these days you can get them for 1000-1500 rubles at any garden shop). You set the timer for early morning or evening, and the system works automatically. Greens also grow well with drip irrigation, though you can keep it simpler for those - a regular hose with micro-perforation will do the job.
The only thing - if you have water from a well or borehole on your plot, make sure the pressure is strong enough. If the pressure is weak, you'll need to buy a small pump, but that's a one-time expense. Honestly, it's so much more convenient than driving out there every single day in summer, especially when you've got a little kid at home.