Pick the kids up from hanging out with cousins. Barely in the car and it starts. "Why don't we go on vacations" "When are we getting a pool" "I want to go on a fishing trip too!". Just a outpouring of GREED and ENVY.
Your children are young. They don't understand how expensive it is for vacations, etc. Not necessarily greed, and envy is natural for us all.
Like Baymule says, set up some fun stuff for them to do. Make it a summertime hair color party and invite the cousins. Coloring on the white sheep is perfect. (Unless you are showing that one any time soon.) I bet the in-laws will get tired of hearing about how you are the cool mom/aunt that colors their cousins' hair to celebrate summer vacation. LOL If the cousins live fairly close and have a pool, plan more trips to cousins for kids to enjoy THEIR pool. No upkeep for you!
We are/were a one income famiy too. I grew vegetables and fruit and canned everything we ate except beef and pork. We ate rabbit (homegrown) instead of chicken and raised our own eggs. Made all our food from scratch. We never went out to dinner or took any vacations. Bought used cars, used furniture, clothed the kids in used clothes donated to us by wealthy church friends. Washed diapers and hung them on the clothesline - paper diapers were too expensive. The kids loved opening the bags to see what we got! Some of their favorite outfits were out of the bags. This was before moving to our present home where we hoed extra acreage would allow larger gardens and orchard. NO! The soil has a Ph of 9, and won't allow anything to grow. After 35 years of putting all the rabbit, goat, & horse manure into the soil, the ground squirrels take it all! LOL But we had ponies and 4-H livestock. They never went to the mall, their friends were jealous of their "farm", they swam in the Doughboy, and I never enrolled them in any summer activities except one week of sleepover 4-H camp, which they paid for by applying for grants and earning the fee.
Your kids are NOT greedy and envious. They are just kids. Just keep saying "No" and explaining you can't afford it right now. They will accept it. You are good parents and they will enjoy their lives on your farm. Having a mom that is home is worth more than fancy vacations and pools.
And look into those Imtex pools. You and DH could be floating in a blowup chair sipping a cold beverage while the kids do the chores.

Nothing wrong with talking to your kids about saving for a pool, or waterpark trips, etc. They will understand if they are saving their own money to use on stuff. Our kids had ponies and livestock, so Christmas gifts were often "need to be replaced" tack and show equipment with one or two fun toys. Our pool was an 18'x32' Doughboy which we brought with us from our previous house and had set up at the new one. The kids learned to swim in it and had just as much fun until they were teens. Then they joined the public pool swim teams which also led into jobs as locker attendants, etc.
We plan to put up an Imtex portable pool in Yantis. We saw them in Texas for $800 - 15' x 25' x 5' deep. DS3 bought one to put up for his kids last summer. Easier to put up than Doughboys. He took it down and stored it over the winter and said it was easy to do and well worth the price. With the Doughboy types you can replace the liners when they spring a leak. They usually last several years, but when they need replacing our liner was $1000+ and we had to pay $500 extra to have it installed due to size and weight. Doughboys are semi-permanent and stay up all year which means a massive cleaning job in the spring. You have to leave it filled or the liner will shrink. Covering it is cumbersome and our heavy winds ripped the cover off. The Imtex pool probably has to be replaced every 4-5 years if you can't repair the liner (the liner kits work well for smaller leaks) but it should hold up for several years. Ask the kids what they are willing to give up for a pool and set up a savings jar for it. You might find them on closeout sale at the end of summer, and buy it as a family Christmas gift for installation in the spring.