How old is your child ?

Yes, it's virtually the same process,, you need to apply for a settlement visa for him, as you have ILR already and he's your dependant he will be given ILE (which is the same as ILR)

Yes there is a possibility of rejection, because the Embassy could say that your mother has 'sole responsibility' , (search on here for it),

Good you send him money but its more than that, you need to provide as much evidence as possible you have sole responsibility and not your mother.

This gives you an idea, thou some of it doesn't apply to you as your husband is the child's father.

Get the sole responsibility right and you shouldn't really have a problem.

14.5 - "Sole responsibility"
In order to fulfil the 'sole responsibility' requirement of the Rules, a sponsoring parent must be able to show that he or she has been solely responsible for exercising parental care over the child for a substantial period. This is in contrast to the concept of the ordinary family unit where responsibility for the child's upbringing is shared between both parents.

You will need to be satisfied that the sponsoring parent has consistently supported the child, either by direct personal care or by regular and substantial financial remittances.

If the sponsoring parent and child are separated, the child will normally be expected to have been in the care of that parent's relatives rather than the relatives of the other parent. This means, for example, that an application by a child to join his/her mother in the United Kingdom on the basis of sole responsibility should normally be refused if it transpires that the child has been in the care of his/her paternal relatives and that the father lives nearby and takes an active interest in the child's welfare.

The following factors should be considered in assessing sole responsibility:

If the parents' marriage/civil partnership has been dissolved, one of the parents must have been awarded legal custody, which includes assumption of responsibility for the child. (You should take care to ensure that the issue of a settlement entry clearance to the child will not contravene the terms of the custody order). Annex 1 contains a list of those countries whose custody orders can be recognised as valid in UK.
Does the marriage / civil partnership subsist, but the parents do not live together?
Are the parents married / in a civil partnership?
If the parent migrated to the UK:
how long has the parent been separated from the child ?
what were the arrangements for the care of the child before and after the parent migrated ?
what has been/what is the parent's relationship with the child?
By whom, and in what proportions, is the cost of the child's maintenance borne?
Who takes the important decisions about the child's upbringing, for example where the child lives, the choice of school, religious practice etc?