having a second job will almost certainly affect your car insurance premium, but this depends on just what the job is. Most don't present a problem but there are some jobs that insurers consider to be so risky that they impose large additional premiums, or even refuse cover at all.
The first thing to consider is that someone with two jobs will possibly do twice as much commuting as someone with just one! Commuting, particularly at peak periods and weekends, can lead to traffic accidents when people are in a rush to get to work, and there are lots of cars on the road. This increases the risk of the insurance company having to pay out on a claim and so the premium is likely to rise.
Some part-time jobs, though, involve even greater risk. Someone who worked evenings for instance may be driving during the most risk prone times of the day. There may also be alcoholic temptations after finishing work at night. All of these push up the risk profile.
One of the worst part-time occupations that anyone can have, from an insurance company's point of view, is a DJ! Whilst this can be a fun job to have, it sometimes involves late nights and the consumption of alcohol.
Tiredness can also be an issue for those who may be working for longer than the number of hours that most of us consider to be reasonable. this can lead to lack of concentration and a higher risk of accidents.
It is unusual for insurance to be refused completely because of a second job however; so if you have been turned down, and given this as a reason, there may be other factors at play or you may just have been unfortunate in your chosen occupations. In either case you may find a chat with an experienced broker to be very helpful to you.