It depend on the immigration. I did read that some immigrations accept only request within the last week. Its always best practise to check the local requirements first. With 70+ immigrations there are many differences.
You need a consent letter from your wife to travel with your child: ref Thai embassy in Bern :
1.2) Only one parent travels with the child/ren; please provide
- An official relationship document, e.g., birth certificate
- consent letter* from the other parent/legal guardian with a copy of his or her passport OR if you have sole custody, you must provide a copy of custody papers OR if the other parent is deceased, you must provide a copy of the death certificate.
Get a proper visa for longstay if you intend to longstay. For some not working, studing or being retired in Thailand it means the only option is a more expensive Elite visa.
Its not only the financial issue. For me the paece of mind knowning i can go anytime and not need to worry about getting my 2th or 3th re-entry in time made me just get the multiple. Only if i am sure its only 1 time i do a single. But nothing wrong to look at the financial side.