First of all, you're not a failure. We all feel like that! If there were a magic formula, some mom would have the Nobel Prize by now. Instead, we have mile-long sections in the bookstore with everyone's different opinion on how to do this!
You might consider a bit of a structure in your house so the 4 year old knows what to expect and so that activities vary. The 2 year old may be less clingy when she knows there's something fun planned. Not everything needs to be an outing - kids don't always transition well, and they may pick up on the inevitable hassles of getting all the stuff together and hitting the road.
Preschools and Pre-K and kindergarten all have schedules, as do camps and day care - free play on arrival followed by circle time followed by snack followed by arts & crafts followed by recess/outside play, then quiet time/story time. Or some variation of that. That doesn't mean it's not relaxing and fun - there is value to structure without it being rigid.
What if you instituted something similar? Free play in the morning followed by breakfast, followed by everyone taking their dishes to the sink and maybe helping to load the dishwasher. Many hands make light work - this is a good time to teach that. If everyone cooperates, we get more done. If everyone clings and whines, we get nothing done.
First, look at the weather forecast for the next day. Decide what's an appropriate activity (beach or library, park or museum?). Tell the kids the night before what you have on the schedule. If it incorporates something they have asked for or enjoyed before, great.
Next, give a head's up when it's going to be time to transition to the next thing. The 4 year old may be able to use some cues, like the digital clock on the cable box or a regular clock. Or you can set a timer, most of which have a 5 minute warning buzzer. Let them know it will be time to clean up the toys and get ready for X when it buzzes the second time.
If the 4 year old is teasing the 2 year old, she goes to her room for some private time. They may both be craving your attention with the teasing/clinging routines, but don't let that make you feel guilty or throw you off track. Let them know you want to spend time with them and enjoy the beautiful summer, and then say "Here's how we're going to do that."
You don't have to be rigid once you get to the planned activities. A planned day in the park doesn't mean every swing or seesaw is planned. A day at the museum doesn't mean the exhibits are dictated. If they don't have the attention span for that, then make the children's department of the library your destination. Get them psyched about being able to pick out a book of their choosing. Libraries often have play areas and puppet areas and story time and computers - so there can be something scheduled surrounded by free play, then you all come home with a book. Get them their own library cards. The 4 year old will think that is awesome. Bring the books home, read them together or separately, and be sure you get one too!
Outside time can be scheduled but still open. My neighbor has kids 2 and 4, and every day they take a nature walk (each kid with a bucket) to see what they can find. Sometimes it's a neat leaf to trace or put between layers of wax paper, sometimes it's a bunch of rocks to wash off and paint (make into paperweights for relatives!), sometimes it's a used up bird's nest, sometimes it's a bunch of sticks to turn into a design. Sometimes it's just watching a toad and chasing chipmunks, with nothing to bring home.
Try to have fewer expectations for a beautiful and perfect relaxed summer - that's a fantasy! Scale back the excursions in the car if the kids just aren't patient enough, and let them know that, if they don't like that, it's fine with you if you stay home and do nature walks. If you put too much value on the destination activity, there's plenty of room for their attention span to end before you even get there. Try changing the way you see these activities, and see great value in the stuff you do together even if it's in the kitchen or in the yard. You'll go easier on yourself, and you won't be so frustrated.