Vienne - you state your agent is estimating $19k in closing costs on the home you're selling, I'm assuming this amount doesn't include the realtors commissions you're also paying? This estimated amount works out to be roughly 6% of your sales price, which happens to be the maximum amt a seller can contribute towards buyer's closing costs for an FHA loan............
And if you're also purchasing another home, and you're being asked to pay those closing costs, I wouldn't blame you if you felt like you're getting a double whammy!
However, closing costs, and the perception of who should pay for what, don't tell the whole story. If the prices you're paying and receiving on your respective homes seem fair, if not great deals to you, and if your buyers can actually close on the home your selling, then consider these strong compensating factors.
If after you've stepped back and looked at your picture, and the closing cost matter still doesn't seem fair, then make sure to let your agent(s) know your feelings!
good luck, and let me know if I can provide any further details relative to your situation!
best, Jeff Marr