Hi tres. I notice we are both called "happy", I wonder if we're related?
I think it's very nice that you have an interest in your nieces and nephews. Extended family can be a very positive influence on kids and also help give the parents a much needed break. I think it's sad that you are wanting to spend time with them and the mother/mother-in-law is being given preferencial treatment over you. Having said that, I am not surprised. Many parents of young children can be very protective about the quality of care that the children get by anyone other than them. It may not be a case of them not wanting you to spend time with the children rather they may simply have more confidence in the mother/mother-in-law since she is older and (presumeably) more experienced with the children.
I would suggest that you make (more) attempts at finding occasions where you can spend time with the children but in your brother and sister-in-law's company. This does not include large family gatherings but occasions where you are exclusively interacting with the children but in the parents company. Doing this often will hopefully give the parents the confidence in your "parenting" abilities that they clearly need and you desire.
I wish you well and as a parent myself congratulate you on caring enough about these children that your heart aches to spend more time with them. They are very lucky to have you as a relative.