I am unclear on whether you want to keep the first house or not. If you are looking to buy and keep your current property, It won't be that big of deal as long as you can attain the financing. If you want to sell your current property and buy another, proceeding in the wrong order can be a costly mistake. Depending on how long you have owned the current home and whether you are upgrading or downsizing, you may also want to consult a tax advisor to make sure you don't take any tax hits.
If your scenrio is to purchase a replacement property contingent upon selling your existing property then it gets a little more difficut and can be done. Most of the time a rentback is not the way to negotiate as the new buyers of your home want to move in right away. Lenders for the most part will not allow more than a 30 day rentback. In my buyer's contract I negotiate that the seller give my buyers at least 2 weeks to sell their property before the 72 hour contingency takes affect. That way my buyers have a chance to at least get their home in escrow and cannot be bumped by a non contingent offer right away. Of course my buyer's property needs to be priced right. In this market it may even take longer to receive offers for any property depending upon your location and market conditions.
The assumption is that you own a home that you plan on keeping and you want to buy another home (possibly a vacation home). If this is the case, it depends on your financial strength. If you have good credit and your debt to income ratio is healthy you should have no problem. A good person to tell you if it is possible is your banker or mortgage person. Good Luck in getting your second home.
If you plan on selling your first home and are concerned that you may end up with two mortgages, talk to your financial person about a bridge until the first is sold.
Not if you can qualify for the loan. What are you planning on doing with the first home? Selling it down the road, or keeping it for investment property? Will you be renting out your first home for income? You need to post with more information for us so that we know what your intentions/concerns are. Just answer your own question so that we can follow the thread.