Feeling like a bad mom advice

I'm feeling like a bad mom right now this summer. I'm a sahm with three hurt my arm. I'm not sleeping well and I'm with baby and pumping at night. I don't have help so I'm not getting extra rest.

What I have been doing since I don't get rest or a break of any kind is two mornings a week I let my oldest eat snacks and watch tablet for two hours. I fill the fridge shelf with things they like fruits, veggies, yogurt, cheese sticks, granola bars. Then I let them help themselves and watch tablet. While me and the baby still sleep.

I'm just struggling and I feel bad because I normally would be up before everyone and be ready for the day. When I do this I feel like I'm two hours behind my morning schedule of getting ready and getting the baby up.

I'm looking for some advice of how I can rest. My oldest doesn't nap and the two youngest don't nap at the same time so I don't really get a break. Today I'm taking them all to the beach one armed in a sling I'm already overly exhausted but want them to enjoy their summer. Is it normal to be a bit lazy sometimes as a mom and sleep in when two kids are awake and occupied?

It's been seven weeks they have done all the pools sprinklers and movies. My issue is how do I handle the exhaustion and deel with being sleep deprived. Everything takes me twice as long to do with one arm and my kids do not have patience.