You can only get pregnant around your ovulation. The egg dies pretty quickly after ovulation if not fertilized (10 to 24 hours). The sperm can live inside you for a few days (3 to 5 days) to wait for the egg to be released. So to get pregnant from sex right after your period your ovulation should be unusually early meaning that your cycle will be short (around 21 to 23 days long).
You can test from the time you miss your cycle. A lucky few women will get a positive result even a few days before that with the early detection kits but it is not guaranteed. The most accurate and reliable tests are about 7 days after a missed period.
I have real empathy with you for finding time for sex with 2 young kids to look after. It is important for your marriage and it is also important that you both have fun doing it and not just because you want to make a baby. If you only do it to make a baby it becomes another household chore and gets old pretty quickly.
You will just have to find a way to be alone with your husband when you need to. This might mean odd hours, strange places, shutting your door or sending the kids for a sleepover.
Best of luck!!