2 years will not be enough to learn reading and writing of Chineses.
Depending on the age, 3 years is minimum to learn reading and writing.
Unless your two kids are twins, you will need to stay in China for at least
4
-5 years to achieve your goal.
Speaking can be taught by you at home. Keyword: read Chinese books to your
kids everyday. Daily life utilizes very limited vocabulary thus reading is
necessary.
Seems your husband is also Chinese? Then you can speak only Chinese at home.
Why must It be mainland China? If your primary goal is for kids to leanr
Chinese, you can go to HK, Taiwan, or Singapore, especially Taiwan. Your US
citizenship will be less of a barrier there.
If you have sufficient income in U.S., you can hire private tutors for
Chinese. Weekend school is not enought. During summer, take them to China
and stay for 2 months in a pure Chinese environment.
As long as you and your husband both work, your household income can afford
this.
I suspect you are using this as an excuse to escape the pressure of Job
hunting upon graduation? Sorry if I am wrong...
Life is not easy at our age (small kids, career just starting), but overall,
life is harder in China for average people.