"will I be denied benefits because I quit and did not accept their offer to come back?"
Most likely yes. Voluntarily quitting a position and then turning down viable work that you are capable of doing are the kiss of death in collecting UI benefits. The first key element of collecting is that you lose the job through no fault of your own and you didn't you resigned. Your child care issues are not your employer's problem. It was your choice to quit when you could not work it out.
You also were doing some work for the prospective employer. Even if it wasn't full time work it does have to be reported to UI as well and it does offset any benefits that you might collect.
"Also, how long can a claim be reviewed before a decision is made?"
As long as the state needs. They are the ones who have to pay and if they need more information than they take all the time they need. With the large numbers of people out of work and collecting.
"Is there anything I can do? "
See if that contract work is still available. It would pad that savings account. It doesn't appear you are eligible for UI benefits.