My spouse has a criminal record

A person's past is NOT always relevant in a custody case involving minor children.

If a person was convicted many years ago, it might not even be allowed to be mentioned to the judge.

If your spouse (say wife) was convicted of selling drugs 15 years ago, you married her 10 years ago (and knew of the conviction) and all of your children are under the age of 5, her former criminal record might be irrelevant. If her record has been clean for 15 years, it shows that she has probably cleaned up her act. If she was such a bad person, then why did you marry her?

If a person was convicted of writing hot checks, how does that show he is a bad parent?
That person might not be crummy at math or is irresponsible, but hot checks are a lot less important to a judge than driving while intoxicated, beating up people, threatening people with a weapon, threatening to kill their spouse, injury to a child, etc.

If a person has been convicted of DUI or DWI within the past 2 years, it might be VERY important. Has the person finished their probation successfully? Is the person attending AA meetings? Does the person admit to a drinking problem? Do they still drink? Do you have evidence that the person is still consuming alcohol? If so, what evidence do you have? The burden is on you to prove that he is still an alcoholic, still actively drinking, still drinking while drunk, not admitting to having a problem, falls asleep when they are supposed to be watching the child(ren).

People can and do change. If the judge feels the person accepts responsibility, has worked hard to not repeat the same mistake twice and has taken steps to never repeat the same mistake, the judge might decide that the past is behind the person and they have learned their lesson.