You won't get that loan approved.
First of all, you cannot use a part-time job as income for ANY mortgage loan unless you have had the job for two full years.
Second, unless you have seen a copy of his credit report, you have no idea if these allleged "small things" will come up or not...you need to find that out first.
Third...banks consider $1,000 a month poverty level for ONE person..if your husband is supporting 4 people on that income including himself and makes $1500 gross, that means he takes home LESS than that to support 4 people.
I don't think you have really thought this through...home ownership isn't like renting...if the water heater breaks, you fix it...if there is a leak, you fix it...you have to pay property taxes, hazard insurance, overall upkeep....where is all that money going to come from? You have two kids...do you have money for emergencies with them???
Low income individuals SHOULD be renting so they have a FIXED expense.