Figure out how much you own
You say that one property is 65% of the value of the two properties and the other is 35%. But how much of that do the two of you actually own? If you have co-signed mortgages on both properties, then your equity is going to be lower. If you sold both properties, then your take away would be just half of that equity. And while the 35% property may be less valuable, if you bought it first, it may actually have more equity.
It's the equity that matters here, not the value of the property. With a mortgage, the bank is more of an owner than you are until you've paid down most of the loan.
You may find that the bank won't agree to a single-owner refinance. A co-signed mortgage is a lot easier for them to collect, as they can hold either of you responsible for the entire loan.
Consider selling the 65% property
If you sell the 65% property, then you can pay off any mortgage on that property and use the equity payout from that to buy out your relative on the 35% property. If you currently have no mortgage, you'd even have cash back. This is your fewest strings option.
15% mortgage
Let's say that you have no mortgage now. So this mortgage would be the only mortgage on the property. It's not so much, as 15:65 is 3:13 or 18.75% of the value of the property. That's more of a home equity loan than a mortgage. You should be able to get a good rate. It might reduce your short term profit, but it should be survivable if you have other income.
If you don't have other income, then seriously consider selling the 65% property and diversifying the payout into something else. E.g. stocks and bonds.
Private mortgage
Perhaps your relative would be willing to float you the loan. That would save you bank fees and closing costs. Write up a contract and agree to take assignment of the title at payoff. You'll need to pay a lawyer to write up the contract (paying a modest amount now to cover the various future possibilities), but that should still be cheaper.
There's a certain amount of trust required on both sides, but this gives you some separation. And of course it takes your relative out of the day-to-day management entirely. Perhaps the steady flow of cash would provide what they need.
Management fees
If your relative is willing to remain that involved, that can work. Note that they may not want to do this, so don't get too attached to the idea. Be prepared for a no. This would be a great option for you, as you pretty much get everything you have now. They get back the time meeting with you to make decisions, but they also give up control over those decisions. Some people would not like that tradeoff.
The one time I was involved with a professional managing a property for me, the fee was around 7% of the rent. If that fits your area, you might reasonably charge 5%. That gives a discount for family and not being a professional.
There's a relatively easy way to find out what fits your area. Look around and see what companies offer multiple listings. Call until you find a couple that will do management for you. Get quotes for managing your properties. Now you'll know the amounts.
The big failing though is that this may not describe the issue that your relative has. If the real problem is that the two of you have different approaches to property management, then making you the only decision maker may be the wrong direction. This is certainly financially feasible, but it still may not be the right solution for your relationship.
If you get a no on this, I'd recommend moving on to other solutions immediately. This may simply be too favorable to you.
