It seems very clear to me that you should sell it.
No lender will consider it an advantage, and some will lend you less because you have outgoings. So there is no disadvantage in selling it.
But there are huge advantages in selling it. First of all you will have more cash. This means that you will have a smaller mortgage when you buy a house. So you will need to borrow less. If you are borrowing less, then you will have a lower LTV and will pay a lower rate of interest for the duration of the loan.
The blips on your credit record may prevent you from borrowing at 80% LTV or may restrict the lenders who will lend to you. They might be more open if they are lending say 50% LTV.
I presume you are married? If not, then hold off getting married as it seems as if your OH might qualify for a mortgage on their own.
Is there any reason for holding onto the rental?
Without the numbers, it's hard to be definitive.
If you have a cheap tracker, it's possible, but as it's only 30% LTV, then it's unlikely to swing the decision.
You should consider using your OH's savings to pay down your mortgage.
If you are paying 4% on your mortgage, it's costing you about 3% net after tax relief. Your OH is probably getting a maximum of 0.5% after tax in deposit interest. If you view your finances as one, it makes sense to pay off the mortgage. You can always pay the interest to your OH instead. But watch out for any tax implications of this.