First, to be clear, I am ABSOLUTELY NOT diagnosing anything! I have nowhere near enough information to have anything more than a suspicion. Even that suspicion is tenuous at best. In no way should you take my words over the internet as anything other than general information, and you should see a professional for an appropriate evaluation for your child.
If I were you I'd have my child assessed by a Speech Language Pathologist. There may be atypical oral anatomy or physiology. My radar instantly goes up for Ankyloglossia when I hear of buccal pooling, especially with concomitant verbal expressive language issues. At 24 months I expect to be hearing 2-word utterances, an expressive vocabulary of about 200-300 words, and ~50% intelligible speech.
Ankyloglossia is a disorder where the lingual frenulum (the little flap of skin which connects the bottom of your tongue to the bottom of your mouth) is too short for the tongue to do it's work. Often speech and feeding tasks are compromised, and patients may present with an inability to sweep the inferior buccal cavity (area between the cheeks/lower lips and lower teeth) with their tongue. Additionally, since the tongue cannot lift appropriately sound production is compromised. Sometimes there are bilabial sounds present (/p, b, m/), often there is a lack of appropriately articulated front, tongue high sounds (most obviously lingual alveolar plosive phonemes such as /t,d/ since at these ages the fricatives and affricates are rarely present). Usually speech is muffled and garbled, and often children stop talking altogether because they're unable to perform the acts in a way which is intelligible to adults.
A Modified Barium Swallow Study (MBS) is a procedure where a subject swallows a variety of textures with a little barium mixed in to make it glow on the x-ray and the Speech Language Pathologist (many people are surprised that this is in our scope of practice) watches to see if the airway protection mechanism functions appropriately to keep food from entering the trachia. It's rarely used for oral phase disorders.
I would be quite surprised if a modified barium swallow was ordered considering the location of the feeding disorder. Generally these are only performed if there's concerns of aspiration. Most likely there will be an oral peripheral examination. During the exam the examiner will look inside your child's mouth and try to determine if there is a functional or structural problem. There will probably be a small snack involved so the SLP can observe feeding.
Motor planning disorders are rather rare, if I were your SLP I'd rule out disorders involving the oral anatomy first, then move on from there. It's not impossible that there's a motor planning disorder but it's not what my differential diagnosis would immediately jump to considering the symptoms you describe.
The specific specialists you might be interested in contacting would be: Speech Language Pathologist, Pediatric Ear Nose and Throat doctor (Otolaryngologist), or Pediatric Oral Surgeon. I suspect that both the ENT and oral surgeon would want to see a report from an SLP prior to taking any corrective action if atypical lingual frenulum length is discovered. They usually want a letter from me outlining my diagnosis and test results when I have a case like this.