You have my sympathy. 26 weeks with DS2 and I'm still sick every day
the real hyperemesis dropped off at about 14 weeks though.
My tips for feeling a bit better are ...
Mint imperials
Frozen grapes
Lemonade with lot of ice
Butterkist toffee (just one teeny piece at a time)
Lollipops can be quite good too but stick to lemon.
I've also head taking vitB can help.
I fed my DS stuff that didn't smell too much so it didn't set me off. Sandwiches, toasties, pasta and sauce, cold meats, cheese, olives, cucumber etc.
At my worst, DH would make a packed lunch for DS before he left for work so all I had to do was open some Tupperware and a yogurt!
Also, don't worry too much about activities for the DC. Colouring, DVDs, bathing toys, playing in the garden etc are all pretty easy and take minimal supervision.
Go easy on yourself. This will pass 