It is possible. A few conditions must be met though, and after that it’s up to the bishop:
*]You need to be unmarried. If you were sacramentally married to your wife, you will need to receive an anulment before proceeding, if you have not already done so. If you were never sacramentally married, you may need to have your Diocese’s Tribunal declare the marriage Defect of Substanstial Form. This is a Canon Law matter, so I won’t comment because I’m not too familiar with it.
*]Your children will need to be completely unreliant on you. If you have any hand in their current upbringing, you’ll probably be asked to wait until they are old enough to be completely independent.
*]You must be under the maximum age for the Diocese’s policy. Each Diocese sets a policy saying they will not ordain men over a certain age. If you’re too old, you may be rejected.
Many of these cases are very specific to the individual and the policies of the Diocese you are applying to. I would recommend that you speak to your Diocese’s Director of Vocations ASAP to start working things out. His contact information can usually be found on your Diocese’s website, or from your pastor.