You have options but....The only safe way to do this is to find ways without risking the family finances. Before I give this answer let me first say you should have representation in the transaction by a licensed Realtor (c). I would be happy represent you as Buyer Agent free of charge on your behalf.
Option 1 that would allow you to purchase the home with the contingency of your home selling. With so much inventory on the market sellers are having a difficult time finding buyers and are more apt to allow a contingent offer. What this means is that you will need to list your home with a Realtor (if it's only for sale by owner now that won't fly). The reason I say this is because the listing agent (of the home you want) will tell the seller that unless buyer's home is listed on the RMLS with a motivated price it would not be a good idea to have his home taken off the Active status. The percentage of Unrepresented homes selling is very low compared to Listed homes. Only a potential buyer who is highly motivated to move his listed home would be a good candidate for seller to consider for his home sale.
A second option (a slim but possible one in a market like this) is a trade. Many agents are not familiar with this older form of negotiating. Seller may be motivated to negotiate a deal to 'buy' your house if you buy his. The deal should be negotiated with a professional Realtor (I would love to help you through this). I wouldn't recommend you allow the Seller's agent to represent you too as buyer. You need to have someone who will look out for your best interests and keep you from being taken advantage of. Your best interests are of high priority. That won't happen when an agent represents both the seller and the buyer in a single transaction. It's best to have two agents working on a transaction such as this. Seller(of the house you want) has his listing agent to help him with the purchase of your home, you should have your agent to help you with your purchase and with the sale of your house. Seller may like this option because if his home is higher priced than yours and yours is a good home and likely candidate for a reasonable sale then it may be one that he wouldn't mind considering for a short term investment He would want to be able to make some money on it so if you are motivated enough to make it worth his while in order to get the house you want , it could work.
A third option is for you to rent out your home and keep it rented for a while so you can show it isn't interfering with your income- to retain eligibility for the new purchase. If you have a lease with option to buy and allow the renter to have a portion of his rent set aside as down payment on the purchase (non-refundable of course) then you could very well qualify for the new home and still work both mortgage payments out. You would want to get the renter to qualify for the purchase if possible and could actually have the purchase negotiated to some degree in the rental docs. The docs would be drawn up professionally to cover your interests where the renter is concerned. I could give you recommendations for that. For more details please feel free to contact me via my web site link below. Let's get it done! Best to you. To see my quality service rating (data collected from my past clients by an independent research company) go to http://www.qualityservice.org
type in my name June Lizotte and Oregon