Your question raises two issues. The first issue is the discrepancy in credit scores between you and your wife. The second issue is determining if your wife's income will be included in your mortgage application given her employment gap and status as a self-employed borrower. I address each issue below.
When two people apply for a mortgage as co-borrowers, the lender typically uses the lower credit score between the applicants for the qualification process. The higher the credit score used by the lender, the lower your mortgage rate, and the lower your score, the higher your rate.
So if one co-applicant has a significantly lower credit score than the other, they may end up paying a higher mortgage rate and monthly payment. Please note that if you are married, the lender pulls a joint credit report for both borrowers but this does not change how lenders evaluate your scores.
So the impact of a discrepancy in credit scores for two borrowers depends on the specific scores. If one applicant's score is in the high seven hundreds or above and the other applicant's score is in the mid-to-low 700s, the difference in scores may not be a significant issue because both borrowers have relatively high scores.
A score of 700 or higher usually enables you to receive a lender's lowest mortgage rate, so depending on both your and your spouse's scores, you may be able to qualify for the best loan terms if you apply as co-applicants. When you speak with lenders you can confirm the minimum score required to receive the most favorable loan terms as this guideline can vary.
Another scenario to consider is if one applicant has a high credit score but the other borrower has a low score, which requires them to pay a higher mortgage rate. In this case, the difference in scores may end up costing you a lot of money, plus you may not be eligible for certain loan programs, depending on the specific score.
So if the difference in a couple's credit scores is significant and the applicants are in different credit rating bands -- for example one person has excellent credit while the other person has a below average credit -- then it may make more sense for the person with better credit to apply for the mortgage as a sole applicant. Please note that if you apply for the loan as as sole borrower the mortgage you can afford is only based on your monthly income. Your spouse's income is not included in your loan application which may reduce the mortgage you qualify for.
The second issue -- your wife's employment gaps and self-employment -- likely present a more significant issue when you apply for a mortgage. Most lenders require a two year job history for self-employed borrowers, as verified by the applicant's tax returns. In some cases an employment history of only a year is required if the applicant previously worked in a similar field and earns a consistent amount of income.
The challenge is that when you combine a relatively short self-employed work history with an extended employment gap, my sense is that the lender is not going to include your wife's income in your loan application. A lender may be willing to work with a short job history or a lengthy employment break but both of these issues combined may be too much to overcome.
In this scenario it may better if you apply for the mortgage as a sole applicant because you do not want your wife's business expenses to be counted as debt if your loan application does not include her income.
Use ourTwo Person Mortgage Qualification Calculatorto determine what size mortgage two people can afford based on their monthly gross income and debt payments
My recommendation is that you contact multiple lenders in the table below to understand how they would handle your unique situation. Explain your and your wife's circumstances and determine if it makes more sense to apply for the loan as co-borrowers or as a sole borrower. My initial reaction is that it may be best for you to apply as a sole applicant but your circumstances are relatively unusual so you do not know definitively until you speak with lenders.
When you contact lenders tell them you want to have a preliminary conversation about your financing options. Request that they not pull your credit report until you have determined the best approach and you are ready to move forward with the loan.
Mortgage Guidelines for Borrowers with Different Credit Scores: https://www.fanniemae.com/content/guide/selling/b3/5.1/02.html
Mortgage Requirements for Self-Employed Borrowers: https://www.fanniemae.com/content/guide/selling/b3/3.2/01.html