I had a similar situation in my family. When my sister was in kindergarten, she could either move on to pre-1st or 1st grade. My sister's birthday was right at the cut off, so she was the youngest in her class, started when she was 4 and will graduate when she is 17. Due to her age mostly, she was given the option of going to pre-1st to give her time to develop both in maturity and academics. My parents decided to go ahead and send her on to 1st grade and she has done well ever since.
Your son has a lot of things going for him. Since he has a sibling around the same age, that might help motivate him to learn and to stay a grade level ahead. You're a stay at home mom, so that might give you some more time to focus on helping your son stay on course and to help him work on his reading and math during the summer. Your husband will be coming home soon (I'll be praying for him until he returns) and you mentioned that the teacher said she saw progress after he came back in February. You also said his grades have only started falling since the beginning of this month, so it does sound like you were right in that he's getting tired and ready for the summer.
All that being said, I think your son will do better in the long run to go ahead and go to 2nd grade. Because this school is more advanced, it stands to reason that each of the grades will be more advanced, so getting behind early might hurt him more than help. Also if he stays behind, if you transfer to another school that is not so advanced, your son may be so far ahead that he is bored and his grades may slip. You have the whole summer to work with him and if it doesn't help, you do have the option of sending him back to 1st grade later on in the school year. I'd try to avoid testing for a learning disability unless it is absolutely necessary. It sounds like there are a lot of personal things (dad gone, moving to new school, sibling at same level) that are contributing to grades and learning more so than actual learning ability, but you know your son, so do what you feel is right.
Everyone's opinion is just that, an opinion. We can only see what you have written, so really listen to your family members and your heart. I'd also talk to your son and let him know his options and let him weigh in. Let him know if he goes on to 2nd grade, it's going to be hard work, even during the summer, and let him think about that. His attitude will make a big difference, so if he's on board, it'll be much easier for you and your family regardless of which decision you make. I know you will make the best decision for your son that you can, so good luck with whatever you choose!