Repairing Holes in a Baby Blanket?

This may be a time to find a soft fabric and stitch it to the blanket, covering the gap and in an applique style.

The blanket fabric looks much to fragile to cinch it together to see. That risks more damage.

I can find you some good how to applique videos on YouTube if you need them!

I do not believe your blanket is repairable but you may be able to place a new layer of cloth over the entire piece.
Search Google for a quilting or sewing class in your area (your zip code) and take it to one of these places to see if you get someone to help you.

You might also try asking for help at your Michael's or JoAnn's as they usually have people's cards that do this type of work.
It may cost to get it repaired but it then would be like new.

I would try embroidery thread (s) with large needle . You can try to match the stitch width or length to blend better. Hand stitch not machine.
If all fails put it in a shadow box perhaps with other memorabilia. ( baby shoe.,hair etc)

They have iron on fabric pieces, also you could attempt to sew by hand mending the torn/holes securing with a tight knot!

I would try hand stitching a piece of fabric underneath to maybe hold up the areas that are ripping. Maybe using some clear hot glue if it wont hold a stitch.