Congrats on being pregnant, and sorry to hear about the terrible morning sickness.
I am about 15 weeks pregnant with my 3rd child, and my morning sickness and all common pregnancy symptoms also started right before week 4. My morning sickness was absolutely AWFUL...all day, all night. I am still quite nauseated at times, but it got a lot better last week at week 14. I can now eat much easier and foods and smells do not make my stomach turn.
I do not have a toddler like you, my two are already in school, so I had it easier than you do. I rested, rested, rested whenever possible, it was all I could do to help the nausea.
I have heard that acupuncture is VERY helpful, but I can't afford to go. If you can afford it, do it!
Also, I drank gatorade rain instead of water. During the worst phases, water actually had a nauseating "taste" to it, and I could barely keep it down, but gatorade was okay, and the rain version is not as strong as the normal version.
I ate very high fat, high protein healthy stuff like eggs, refried beans, cheese, and avocado when possible, those always seemed to go down okay.
And when I couldn't seem to eat but knew I had to do something, I ate melon (watermelon, cantaloupe, honeydew). Those seemed to help the nausea too.
The last thing I did was always carry Altoid Sours with me. Those got me through trips to the grocery store without puking in the aisles.
Lastly, a lot of the common things they say to eat, like ginger, soda crackers, and pretzels made my nausea much, much worse. You have to figure out what works for you, and it sometimes changes from week to week!